The work of Stirling, as all heat engines, is linked to the temperature difference between hot spot and cold spot; is important as well the mass of the working fluid.
Raising the temperature can easily get the point fall in the use of special materials, high costs.
Lower to the temperature to near ambient can be achieved with good heat extraction systems from cold spot.
You can certainly use a cooling circuit to lower the temp. of the cold spot more, but we are sure that the Stirling engine produces enough energy to run the refrigeration compressor?
The ammonia compression is a really heavy work of pneumatic pumping, and in not many high efficiency.
But there is a second type of ammonia refrigerator that makes use of an absorption cycle—ammonia dissolves extremely well in cool water but not so well in hot water. In an absorption cycle refrigerator, a concentrated solution of ammonia in water is heated in a boiler until most of the ammonia is driven out of the water as a high-pressure gas. This hot, dense ammonia gas then enters a condenser, where it gives up heat to its surroundings and becomes a cooler liquid. The liquid ammonia then enters a low-pressure evaporator, where it evaporates into a cold gas. This evaporation process draws heat out the evaporator and refrigerates everything nearby. Finally, the ammonia gas must be returned to the boiler to begin the process again. That return step makes use of the absorption process, in which the ammonia gas is allowed to dissolve in relatively pure, cool water. The gas dissolves easily in this water and thus maintains the low pressure needed for evaporation to continue in the evaporator. The now concentrated ammonia solution flows to the boiler where the ammonia is driven back out of the water and everything repeats.
Well, the real question is, how rapidly can adsorption remove the heat from a stirling engine? I am not sure of how to scale an adsorption system to fit a specific size stirling engine. What BTU rating are the average RV fridges? All the ones I have seen were old and only reached 45-50 deg F. I imagine if it were coupled with a stirling engine, it would make a nice cryocooler. I just don't have an idea of what the average efficiency of such a system is.
That's beyond my knowledge, I know my rv fridge freezes the whole fridge up solid if I crank it up (3cuft)... The aussie designed solar fridges we're planning to buy (3 way, 12v, solar heater, LPG) are supposed to be way more advanced than the RV fridges and they're full size fridges; designed to run primarily off solar heating.
Is evident that I do not have enough knowledge in description of ammonia absorbtion cycle, ...and overall in English language.
But you are sure that you do not need power to pump (excuse me: not to compress) fluid and actionate a fan that remove heat?
May be that all power made from Stirling engine is necessary for actionate the absorption cycle, or quite, or instead ..even.
Good however the idea to consider two systems: the Stirling that produces waste heat, and the absorbtion cooling that utilize waste heat.
If there isn't a fresh substantial power output, .... in losses, frictions, air turbolences and so on,...may you have only a production of heat.
Each cooling system does not produce cold: By means of an external job moves heat from one point to another, to effect the movement a place become colder.
Has to to be removed much more heat than the moved one, you've to consider losses to effect the own efficiency of the system.
Ma c'è un secondo tipo di frigorifero ammoniaca che fa uso di un ciclo di assorbimento e ammoniaca si scioglie molto bene in acqua fredda, ma non così bene in acqua calda. In un ciclo frigorifero ad assorbimento, una soluzione concentrata di ammoniaca in acqua è riscaldata in una caldaia fino a quando la maggior parte dell'ammoniaca è spinta fuori dall'acqua come un gas ad alta pressione. Questa calda, gas di ammoniaca denso entra poi in un condensatore, dove cede calore all'ambiente circostante e diventa un liquido di raffreddamento. L'ammoniaca liquida entra poi in un evaporatore a bassa pressione, dove evapora in un gas freddo. Questo processo di evaporazione attira il calore e l'evaporatore refrigera tutto nelle vicinanze. Infine, il gas di ammoniaca deve essere restituito alla caldaia per iniziare il processo di nuovo. Questo passo ritorno fa uso del processo di assorbimento, in cui è consentito il gas di ammoniaca a dissolversi in relativamente pura, acqua fresca. Il gas si scioglie facilmente in acqua e mantiene quindi la bassa pressione necessaria per l'evaporazione di continuare nell'evaporatore. L'ora soluzione concentrata di ammoniaca flussi alla caldaia dove è guidato l'ammoniaca indietro fuori dall'acqua e si ripete tutto.
The ammonia absorption systems I'm familiar with have no moving parts or pumps, just a heat source... Minor exception, the big fridges we're looking at use some small fans for circulation.
Grazie per la traduzione!!, ora ho compreso, grazie!! E' un sistema di raffreddamento che utilizza la circolazione spontanea di ammoniaca invece di quella di acqua.
Buoni vantaggi: il cambiamento di stato (evaporazione) del fluido (assorbimento di calore) a bassa pressione.
Svantaggi: la complessità (tipo di fluido, dimensioni) dell'apparato, il contenuto termico del fluido.
Thanks for the translation!, now I understand, thanks! It 's a cooling system that uses the spontaneous circulation of ammonia rather than water.
Good advantages: the change of state (evaporation) of the fluid (heat absorption) at low pressure.
Disadvantages: complexity (fluid type, size of apparatus) to remove the necessary heat.
Why use an ammonia absorbtion cooler to run a Stirling engine, when you can just use a gas expansion engine, e.g. "steam engine", in place of the gas expansion valve in the cooler line?
I fear that in order to simplify the system, starting from the cold part simply ubmerged in a bucket of water, we end up building a ton of equipment to get 100 watts.
Mysore Ammonia was the first in India to start a Cylinder Filling Plant for Ammonia in 1979 and in 1984 was the first to start a Liquor Ammonia Manufacturing Plant in India. With a Long-Term outlook focused on Service, Quality and Safety, in the Ammonia Industry, Mysore Ammonia is known for Transparency in their interactions and good HR practices. Only Indian Company sourcing Ammonia from the overseas besides India, and also the only Indian company with Manufacturing Plants and tie-ups for Production of Ammonia overseas, Mysore Ammonia is highly reputed in the industry for their Supply-Chain Management also. They follow their commitment to provide solutions as per customer needs and deliver where the Customers needs the Product; when they need it, and with consistent Quality & Quantity standards.
After I built my Ross Yoke ALPHA motor, I coupled it to my horizontal BETA motor via belt and pulleys, and after 20 minutes the temperature of the hot cap on the ALPHA motor dropped 40*C, from + 20*C to - 20*C, the motor driving produces about 5 Watts at the crankshaft. If a jacket of some sort was place around the hot cap and a loop of metal tube to and from that filled with a refrigerant (even saline) a refrigeration system could be made. More power, more cold.


text:
Q: default value for chunked field - (setChunked) I am seeing this:
https://vertx.io/docs/kdoc/vertx/io.vertx.rxjava.core.http/-http-server-response/set-chunked.html
vertx.createHttpServer()
  .requestHandler(req -> {

    if (req.method() == HttpMethod.GET) {

      req.response().setChunked(true);

    }
 })

I would assume chunked is true by default but I can't find the default value in the docs. Does anyone know what the default value is?

A: setChunked sets the transfer-encoding header to chunked.
When you send some content to the client with the write method, Vert.x verifies that either the transfer-encoding or the content-length header is set.

A: Do add on the previous answer, you can see the actual code here:
https://github.com/eclipse-vertx/vert.x/blob/f68ae15171053d343590e54884ec377f095ba6b3/src/main/java/io/vertx/core/http/impl/HttpServerResponseImpl.java#L142
public HttpServerResponseImpl setChunked(boolean chunked) {
    synchronized (conn) {
      checkValid();
      // HTTP 1.0 does not support chunking so we ignore this if HTTP 1.0
      if (version != HttpVersion.HTTP_1_0) {
        headers.set(HttpHeaders.TRANSFER_ENCODING, chunked ? "chunked" : null);
      }
      return this;
    }
  }

redpajama_set_name: RedPajamaStackExchange


Hello, It's Kerry aka Leather Babe!!!
Hello everyone, I am Kerry Lynn aka Leather Babe. I am Bill's assistant and I just wanted to introduce myself, it has been a heck of a year already and we have been working hard!
We been revamping this website in case you were wondering why we haven't been doing much on here. The old site was too outdated so that is where I come into the mix of things!
I am the one who has and will be working with Bill to add the newest products, do a lot of the writing and what not and also keep you posted on the latest biker events and advertising. Continue reading Hello, It's Kerry aka Leather Babe!!!
New Look, New Life for Leather Supreme!
Hey everyone, Bill the leather man is back! It's been quite some time since I made a post here. Why you may ask, where ya been? Well I'm still here in Orlando, Florida. My site has been in biz all this time, but it was getting outdated. Okay very outdated!
I was still using PayPal buttons for checkout. The theme was not mobile friendly so it looked like hell on a phone. I just never had time to fix it up right,,, until now. I made a cool biker patch site plus a military patch site.
Continue reading New Look, New Life for Leather Supreme!
Happy holidays from Leather Supreme!
Wow, it's almost Christmas! Time sure flies when your really busy, and boy have I been busy. It's almost the end of the year and once again I have not adding all the new items I want to add in here.
Well, I want to wish everyone who reads my site, and of course everyone who has bought my items a wonderful holiday season. I suppose to be politically correct I should not say Merry Christmas.
But since it's my own damn site I will, so Merry Christmas!! 😀 Also happy holidays and a happy new year which will be upon us in just a few days. I hope you all get what you want and spend the holidays with family and friends.
Continue reading Happy holidays from Leather Supreme!
Hey everyone, I just wanted to wish you all a happy new year! I hope your holiday season has been good and you got what you wanted. I know 2010 was not a good year for many.
In fact for a lot of folks it was the worst year yet, what with homes being foreclosed on and the job situation still bad. I'm sure everyone is looking forward to see what 2011 will bring.
As for myself, I'm not doing too bad. I run around two dozen websites and work from home which I love. I've been doing that for around 4 years now and would not want to do anything else.


text:
global markets|03 December, 2021
Stocks tumble, yields slide after U.S. jobs report as Omicron looms
MSCI global index drops 1% in volatile trade
Traders work on the floor of the New York Stock Exchange (NYSE) in New York City, U.S., October 20, 2021.
By Lewis Krauskopf and Sujata Rao, Reuters News
NEW YORK/LONDON: Global stock markets slid on Friday while benchmark U.S. bond yields fell to a more than two-month low after data showed U.S. job growth slowed considerably in November and markets stayed volatile as investors assess implications from the new Omicron coronavirus variant.
After opening higher, Wall Street's main indexes quickly turned negative with the tech-heavy Nasdaq falling more than 2%. European markets also lost gains and ended lower. MSCI's gauge of stocks across the globe shed 1.02%.
Omicron has gained a foothold in Asia, Africa, the Americas, the Middle East and Europe and has reached seven of the nine provinces of South Africa, where it was first identified. Many governments have tightened travel rules to keep the variant out.
"The top issue is still this whole Omicron variant. There are enormous amounts of uncertainty there," said Randy Frederick, vice president of trading and derivatives for Charles Schwab in Austin. "Volatility means big moves in both directions and we have had a lot of up days and a lot of down days that are both very sizable here just in the last week. ... The market is a bit treacherous."
The Labor Department said U.S. nonfarm payrolls increased by 210,000 jobs last month, well below the 550,000 jobs economists polled by Reuters had forecast, but the unemployment rate plunged to a 21-month low of 4.2%, suggesting the labor market was rapidly tightening.
"On the surface, the numbers came in disappointing because they did not match expectations, but it was not a weak report," said Kevin Flanagan, head of fixed income strategy at WisdomTree Investments.
On Wall Street, the Dow Jones Industrial Average fell 149.72 points, or 0.43%, to 34,490.07, the S&P 500 lost 56.27 points, or 1.23%, to 4,520.83 and the Nasdaq Composite dropped 373.35 points, or 2.43%, to 15,007.97.
The pan-European STOXX 600 index lost 0.57%.
The data caps a turbulent week as investors assess the implications of the Omicron variant and what that means for growth, inflation and ultimately central bank policy.
Markets were also digesting Federal Reserve Chair Jerome Powell's comments this week that U.S. central bankers in December will discuss whether to end their bond purchases a few months earlier than had been anticipated.
U.S. Treasury yields saw choppy trading.
Benchmark 10-year notes last rose 23/32 in price to yield 1.3716%, the lowest level since Sept. 23, from 1.449% late on Thursday.
Currencies also were volatile. The dollar index last rose 0.059%, with the euro up 0.08% to $1.1308. The Japanese yen strengthened 0.33% versus the greenback at 112.79 per dollar.
Crude prices edged higher after producer group OPEC+ said it could review its policy to hike output at short notice if a rising number of pandemic lockdowns chokes off demand.
U.S. crude recently rose 0.65% to $66.93 per barrel and Brent was at $70.48, up 1.16% on the day.
Spot gold added 0.6% to $1,779.73 an ounce.
(Additional reporting by Karen Pierog in Chicago, Dhara Ranasinghe in London, Tom Westbrook in Sydney; Editing by Alison Williams, Will Dunham, Kirsten Donovan and Nick Zieminski) ((lewis.krauskopf@thomsonreuters.com; 646-223-6082; Reuters Messaging: lewis.krauskopf.thomsonreuters.com@reuters.net, Twitter: @LKrauskopf))
((To read Reuters Markets and Finance news, click on https://www.reuters.com/finance/markets))

redpajama_set_name: RedPajamaCommonCrawl


My first own car. Bought the beauty from a friend of my dad. Did its job well and offered cheap transportation, easy to fix and lots of spares by the dismantlers. The poor baby was almost never washed and the picture shows it in a rather clean state. Minor flaws as rust and exhaustsystem breakdown was fixed during the time but when the clutch broke for the second time I didn't fancy fixing it again and we towed it to the axeman.
My first veteran was bought 1999. There are some cars I'd like to have owned and one of them was a Volvo 140. A friend of mine knew this sample, poor looking and converted from automatic to manual. Original B18 engine and a leaking cowlingsystem, constantly keeping bottles of water to fill every 100km... Good thing it's running taxfree in the swedish system as older than 30 years. This became my first "summercar" and I kept it until I found my next Volvo veteran. During the summer 2001 I sold it back to where it came from.
After kissing my beloved 343 goodbye I had to find a substitute for my "wintercar". Once again my friend with the 144 came handy. I found myself owner of my first Volkswagen. This was a rather boring car but also did the job well. After some contact with another car the front was rebuilt. Later I had to scrap it after a taxi made an unplanned move infront of me. By the time I was pretty tired of manual gearbox and promised myself the next car I bought should have an automatic one.
During the autumn 2000, before I knew what to do with the 144 (at the moment parked at my summerhouse), I bought this Amazon. During the years it has gone through a number of "upgrades". First thing when the clutch broke on this one was to change the original B18 to a B20. Flywheel was lightened for better acceleration. I also found new lightglasses for the rear end, original all red ones and rebuilt them to some kind of American style with double twinthreaded bulbs. Rear rims were widened to 6" and some 740profiles on them filled out quite well... The B20 broke down due to previous owner not tightening some crankshaft bolts. Good thing I had another B20 with K-cam. Together with a Weber 36 carburettor I soon had approx 120hp under the hood. Have been collecting parts all the time and for the moment I need time to weld the floor. Until then she's parked.
After my Passat died I desperatly needed wheels to bring me to work. A friend of mine had this Golf which was parked since a year. With oilwarnings and waterwarnings coming on all the time and engine running like a bag of potatoes (!) I brought it to life again. After adding some new fuel and disconnecting the warnings everything worked out very well. During my last years with this one it was sometimes very hard to get it going and it didn't like my girlfriend at all... Preparing for arrival of our son, I got rid of it and started looking for something bigger.
Found this 2.6 automatic after some research. Newest car I ever owned so far. A step in time - 7 years - from the predecessor. V6 and automatic transmission. This is comfort!!! But younger car means more problems when you run into problems... I miss the basic engines and no databox in the Amazon!
Driving the Audi 100 for 2 years and I were totally in love with this member of the Audi family. I thought it was time however to try something even newer. This time jumping 9 years ahead in time! An A6 Quattro 3.0 with Tiptronic, full leather and navigation for a reasonable price were chosen and I hope to stay with this one for a long time.
The needs for a second car became more urgent when I started working weekends again. Found an old E34 diesel with the M51 engine and very smooth running. Quite comfortable and the automatic transmission is really pleasant! Now gone again as needs for a second car also gone.
After staying with the old A6 for more than 5 years now, decision were taken to look for a younger one with diesel engine. After looking at the 3.0 TDi for quite a while, finally found this 2.7 with Tiptronic, full leather and of course Quattro! Comfort raised to new levels... And the diesels sure have torque enough, I can asure you!


text:
Phoenix United States China Beijing National Hockey League NHL Western Conference NHL Pacific Division Arizona Coyotes Robin Lehner Gary Bettman Bill Daly Men's sports Men's hockey NHL hockey Hockey Professional hockey Government and politics State governments Summer Olympic games Business Media and entertainment industry Sports industry Sports team and league operation Sports business Sports Lung disease Coronavirus Health Diseases and conditions Infectious diseases COVID-19 pandemic Olympic games
Bettman: NHL still planning to have players go to Olympics
By The Associated Press - Dec. 10, 2021 06:44 PM EST
Vegas Golden Knights goaltender Robin Lehner (90) skates around the net during the first period of an NHL hockey game against the Calgary Flames Sunday, Dec. 5, 2021, in Las Vegas. (AP Photo/Ellen Schmidt)
The NHL is sticking to its plan to allow its players to compete in the Beijing Olympics.
Speaking at the conclusion of the board of governors meeting in Florida, Commissioner Gary Bettman said Friday the league will continue to honor its commitment to giving players the opportunity to compete for gold in February.
But there is still no clarity on what happens if an NHL player tests positive for COVID-19 in China, including the length of a potential quarantine and if the individual will be allowed to leave the country during that period. Any significant disruption to the NHL schedule also could alter the league's thinking on the Olympics.
"We made a promise," Bettman said during a news conference at the Eau Palm Beach Resort & Spa following the board's first face-to-face meeting since 2019. "It's not like we haven't expressed our concerns. But in the final analysis, subject to some caveats, with all of the issues that are being raised ... the players, for the most part, seem to continue to be saying they want to go."
The league made that promise to the NHL Players' Association when the extension to the current collective bargaining agreement was signed ahead of pandemic-delayed 2019-20 season. The two parties then inked a deal with the International Ice Hockey Federation on the Games in September.
"Our concerns have only been magnified," Bettman said of going to Beijing. "But ultimately, we made a commitment."
Vegas Golden Knights goalie Robin Lehner became the first player to opt out earlier this week.
"We have concerns, and we've expressed those to the players' association," Bettman said. "We've seen that a number of players are now expressing concerns. We'll have to see how this ultimately plays out."
Deputy commissioner Bill Daly said the league could pull out of the Olympics at any point because of COVID-19, but Jan. 10 is the deadline to nix the plan without financial penalty.
The NHL went to every Olympics from 1998 through 2014 before declining to send its players to the 2018 Games in South Korea.
Owners have always been lukewarm on the showcase even under perfect health and safety conditions for a number of reasons, including the disruption to the league calendar.
"I don't think that this is going to be the ideal Olympic experience in terms of the lockdowns in the Olympic Village and everything else that's going on," Bettman said. "But again, we made a promise to the players, and I'm going, to the best of our ability, adhere to it, understanding that there may be consequences that nobody's gonna like.
"But we made a promise."
The other big topic Friday was the evolving Arizona Coyotes situation.
The City of Glendale informed the team this week it intends to lock the club out of Gila River Arena by Dec. 20 if all outstanding debts to the city and the building's management company were not paid.
Glendale city manager Kevin Phelps sent a letter Wednesday informing the Coyotes they owed $1.3 million in taxes, including $250,000 to the city.
"There's no issue with the Arizona Coyotes," Bettman said. "It's clear that the City of Glendale has either an agenda or an edge in the way they're dealing with the Coyotes. I think there was a miscommunication.
"All of the outstanding obligations had been brought current."
When the Coyotes first moved from Winnipeg in 1996, the team shared America West Arena with the NBA's Phoenix Suns in downtown Phoenix. The team moved to Gila River Arena in 2003, but faced near-constant relocation rumors as ownership changed hands.
The team has submitted a bid for a tract of land in Tempe — another Phoenix suburb — in what could be its first step in landing a permanent home. Bettman, meanwhile, said there are venue options for the Coyotes next season if their current home remains off the table.
"The Coyotes aren't going anywhere. ... They're going somewhere else other than Glendale, but they're not leaving the greater Phoenix area," Bettman said.
Bettman said the salary cap, which has remained stagnant at $81.5 million during the pandemic, will rise by $1 million next season. He added league revenues are expected to hit $5.2 billion in 2021-22 — a return to pre-pandemic levels.
More AP NHL: https://apnews.com/hub/nhl and https://twitter.com/AP_Sports


Last Tuesday, 3rd of November, a ceremonial announcement of final results of Nastartujte se competition took place in Hotel Ambassador – Wenceslas Square, Prague.
From more than 50 registered projects DataFromSky got a title of the second best start-up project in Czech Republic. Being a part of Nastartujte se competition was a great opportunity for us and we would like to thank to organizers and all people connected.
We are very proud of our team and we appreciate the award very much. It reminds us that everything we have been working on day by day does make sense and is moving forward.
A Workshop titled Modern methods of image recognition and processing methods was organized recently by Technical University in Liberec*. The aim of the workshop was to offer insight into image processing applications from the industry, as opposed to research setting.
David Herman and Adam Babinec went to present DataFromSky, with a presentation as well as a stand, and talked about the applications and methods behind DataFromSky.
* In case you are curious, the complete chain of institutions behind the seminar is this: Institute of Mechatronics and Computer Engineering – Faculty of Mechatronics, Informatics and Interdisciplinary Studies – Technical University of Liberec.
That's why there are numerous initiatives and organizations working on increasing road safety – eg. International Road Assessment Programme, UN Decade of Action for Road Safety, Inter-American Development Bank Road Safety Strategy, World Bank Global Road Safety Facility, Global Road Safety Partnership of Red Cross and Red Crescent, FIA Foundation – just to name a few. The list goes on and on.
Among other benefits, DataFromSky can help assess safety of intersections. To communicate this easily to the general public as well as potential customers, we created an infographic.
Mike On Traffic is a blog about "the Less Boring Side of Traffic Engineering". DataFromSky was recently mentioned in a post called Counting Cars from the Sky: The Future of Traffic Monitoring.


Well well well, what a horrible night! Tsk!
Didn't get to sleep until well after midnight – then persistent dreams, it seemed like one long continuous one, I reckon it was full of regrets and failure. Yet I once again can recall no details for certain at all.
Around 0420hrs I woke and pondered on the things that needed to get done today.
Out of the £300 second-hand, working rather shakily recliner and off for a WRWW. Little Inchy was still sore.
Into the kitchen to make a cuppa and get the medications ready. Took a photograph at the top of the page, by bravely opening the window to get a better less reflective shot. It surprised me with it not being so cold with the fog stroke mist out there this morning.
Responded to the innards demand, for a WRHD session with trepidations. But all was well indeed! No Haemorrhoid Harold bleeding at all. Anne Gyna was absolutely fine with me. Roger Reflux Valve hardly any bother at all! Duodenal Daniel not the slightest hassle! Even Arthur Itis was in a good mood with me! All this, along with Little Inchy's lesion not bleeding, cheered me up. Good!
Sorted me out and got the computer on, a fresh cuppa and took the morning medications.
A bit of bother with the WordPress gallery not working, but it came back on of its own accord later?
I wondered how I could get to see Jane and Pete and consulted the Google Calendar.
0645hrs now, and I thought (Another rarity there, hehehe!) I'd call Pete to see if we could arrange a meet somehow or other. I conceived that I might catch him on his way to the paper shop and ATM. When I rang, he'd just got back a few minutes earlier. We had a natter, with Pete wisely consulting with Jane in between, and it was decided that they would both come up to see me next Wednesday morning. I was even more cheered up now!
I considered taking up numismatics as a hobby. I've no idea why I said or thought that?
I poddled into the kitchen again to replace the gotten-cold mug of tea.
Got the inspiration to take the few Estima boiled potatoes in the saucepan, out with me in a bag to nibble on my travels.
While doing this, I realised that the vegetables in stock in the Crock-Pot had not lasted well and were ponging a bit.
So I strained them, put them in a bag then into the black refuse sack. Had to leave the porcelain part of the slow cooker soaking in the bowl in the sink.
Spent a while Facebooking and grahicalisationing.
Did the ablution duties, carbolic soap today.
All ready and wrapped up, a quick check on the weather from the kitchen window, and I set off on the walk to the Nottingham Haematology for the Warfarin INR Level Blood Test.
Trudged up the hill and through the Woodthorpe Park and left down to Mansfield Road.
Just a bit of a nip in the mist this morning, but I kept going, and it was not too bad at all.
Up into Sherwood, and right down Edwards Lane to the ring road.
Stopped to take a photograph of the traffic coming up Edwards Lane.
The mist was oddly masking the far scenery, I thought if it comes out alright, I might add this to the 'Moody Photo' Album on my Facebook page later.
Onward, avoiding many Nottingham Pedestrian-Cyclist on the ring road, and arrived at my destination and took a 'waiting ticket' and settled to read my book in the Out-Patients hall.
An hour or so later, after keeping my eye on the roster board, my number came up and I rather foolishly as it turned out, went to the usual 'Blood-Room door to find it locked'? I looked around rather confused, and a chap laughed at me and pointed in a backwards direction indicating this is where I have to go today. Through a mini-maze of corridors and into an entirely different area of the hospital, I found a nurse stood in the hall waiting for me, and she hastened me into a tiny room to have my blood taken. It appears that the usual room had suffered a water leak and could not be used. Hey-ho, How I managed not to notice that each time the dozens of numbers came up and no one went near the old room, I don't know – or the signs I saw on my way out informing us of the change. Hehe!
Went to the bus stop to find a number 40 was due in four minutes, so caught it back and thankfully, up Winchester Street Hill.
This picture was taken near the ring road through the bus window.
Dropped off at the Commercial Laundry and hobbled up, turned left to the apartment.
Back at the flats I nipped in to see Olive and got a telling off or two. Collected her empty jars after a nice chinwag.
Back to the flat, and literally did nothing more of any interest worth or bother than collapsing in the £300 second-hand recliner, for some reason almost entirely worn-out?
Very strange this sudden loss of drive and interest?
It took a while for me find the interest in making something to eat, but this seemed to bring me round a bit.
Made a meal with eyes far too ginormous and big for my stomach. Tsk!
I didn't eat any of the boiled potatoes.
A sudden feeling of inadequacy, valuelessness and almost a depression came over me – but why I don't know.
I did nothing more after that, other than fall asleep, wake up, WRWW, fall asleep, wake up, pass wind, TV on, fall asleep, wake up, but I did have many dreams in between, no detailed facts about them remain.
← Inchcock Today – Sunday 11th December 2016: A most uncomfortable day, but I'm not complaining I say!


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It offers the latest in technological innovation and style. A turbocharger further enhances performance, while also preserving fuel economy. Audi prioritized handling and performance with features such as: a power liftgate, lane departure warning, and the power moon roof opens up the cabin to the natural environment. Smooth gearshifts are achieved thanks to the 3 liter 6 cylinder engine, and for added security, dynamic Stability Control supplements the drivetrain.


text:
Q: ASP.NET Session State Timeout Problem I am trying to detect a session state timeout in my asp.net application and am unable to do so. I have a base class that derives from System.Web.UI.Page as follows:-
public class BasePageSessionExpire : Page
{
    override protected void OnInit(EventArgs e)
    {
        base.OnInit(e);
        if (Context.Session != null)
        {
            if (Session.IsNewSession)
            {
                string szCookieHeader = Request.Headers["Cookie"];
                if ((null != szCookieHeader) && (szCookieHeader.IndexOf("ASP.NET_SessionId") > 0))
                {
                    Session.Abandon();
                    Response.Redirect("~/SessionExpired.aspx",true);
                }
            }
        }
    }
}

All the pages I need session state checking on derive from this base class instead of "System.Web.UI.Page". Also, all these pages have EnableSessionState="True". I have a blank Session_Start() method in my global.asax file if that is relevant at all.
For some reason after the first request, the "Session.IsNewSession" property is always false. It is true only for the first request and then is always false. I have my timeout set to 1 minute. The session never seems to timeout. What am I missing here ?
Also I have implemented a state server in SQL Server 2008. This is not an in-proc session state implementation.
Thanks in advance.

A: Since you have Session_start event in global.asax file, after the session expires, Session_start fired again. that means session Id is already created and so oninit event IsNewSessionId would return false because session Id is already created.
So removing the Session_Start event will work.
Let me know if this solution works for you.

A: An ASP.Net session is started on the user's first request to a server.  This is the only time that IsNewSession will be true.
Calling Session.Abandon() removes the current session, and then if you redirect the user to the SessionExpired page, that will start a new session.
I'm not sure why the timeout would not be firing.  Have you put code in the Global.asax Session_End event to verify that sessions aren't ending?

A: In your application , If no Session_Start event, Then each time IsNewSession would return true for each postback unless until you store some value in session.
Once you store some value in session, the IsNewSession would return false next time even many post back.
Once session expires, IsNewSession would return true till no session stores.


Hi all! My name is Rachel Vinciguerra and I am a master's student of international development and social work at the University of Pittsburgh. This summer I worked on two program evaluations in Haiti: one a mid-point evaluation for a girls' empowerment program, the other a preliminary design of M&E protocols for an emerging foster care agency. Coming from a social work background, and as an American evaluator working in Haiti, it was especially important to me the studies were culturally-responsive and took marginalized groups into consideration as major stakeholders.
Ultimately, it came down to sharing power with these groups throughout the evaluation process. I found that, when we put them at the center of design, implementation, and presentation, results were richer.
Hot Tip #1: Identify marginalized groups.
There are two pieces to this. First, you have to begin with considerable knowledge of the culture and community in which you are working in order to understand specific and, often complex, hierarchies of power. Second, you have to allow that structural knowledge to contextualize your early conversations with stakeholders in order to identify those groups in the program whose voices are not often heard.
Hot Tip #2: Engage marginalized groups on the same level as your organizational client.
Consider how you engage your organizational client as you plan for evaluation. Are they telling you what questions they want answered? Are you working with them to develop a theory of change model? Are you collaborating on the timeline of the evaluation? Now consider the marginalized groups in your evaluation and share power in the same way with them. They may be beneficiaries of the program, but they may also be groups within the organization that hired you.
Hot Tip #3: Ensure evaluation results can be understood by all involved.
It is research 101. Human subjects deserve access to the knowledge and research they help generate and you can make sure they get it. In the evaluations I worked on, this meant translating all reporting into Haitian Creole and communicating the results in the same diverse modalities I had for my client.
Be patient. Be flexible. Be humble. Make and maintain space in your design to be responsive to marginalized groups and be ready to adapt quickly and with humility as needed.
The American Evaluation Association is celebrating SW TIG Week with our colleagues in the Social Work Topical Interest Group. The contributions all this week to aea365 come from our SW TIG members. Do you have questions, concerns, kudos, or content to extend this aea365 contribution? Please add them in the comments section for this post on the aea365 webpage so that we may enrich our community of practice. Would you like to submit an aea365 Tip? Please send a note of interest to aea365@eval.org. aea365 is sponsored by the American Evaluation Association and provides a Tip-a-Day by and for evaluators.
Anushiik (thank you) for this article and sharing the CREA website and resources. Hood, Hopson, and Frierson have a 2nd book on CRE too from 2015. It is a continuation of their first that you mention in the article. Book is here: http://www.infoagepub.com/products/Continuing-the-Journey-to-Reposition-Culture-and-Cultural-Context-in-Evaluation-Theory-and-Practice. It contains likely the LARGEST collection of Inidgenous evaluators to date in one publication for CRE. LOVE!
I loved Tip #2! We often engage marginalized stakeholders in things like appropriate methods, instruments, etc., but much less often in shaping the timeline or the core evaluation questions. What a great reminder – thank you!


text:
All set for anti-sanctions march
25 Oct, 2019 - 00:10 2019-10-25T02:37:49+00:00 2019-10-25T00:02:05+00:00 0 Views
Minister Chidawu
Herald Reporters
ALL is set for today's anti-sanctions march, with Government providing 265 buses to ferry people from the country's 10 provinces for the main event to be held at the National Sports Stadium. Various provinces yesterday indicated that they were also ready for their own events in respective districts.
Speaking at a Press briefing in Harare on preparations for the main event, Harare Metropolitan Province Minister Oliver Chidawu said buses will be available at usual pick up points from 6am.
"We have allocated 100 buses for Harare, Bulawayo 50, Mashonaland West, Masvingo and Midlands will each get 20 buses respectively, while Mashonaland Central will get 15 buses, Mashonaland East, Manicaland, Matabeleland North, Matabeleland South will each get 10 buses respectively," said Minister Chidau.
He urged patriotic Zimbabweans to come in their numbers in support for the lifting of sanctions.
"We thus call upon all patriotic Zimbabweans to come out in their numbers in support of the call for the lifting of these unjustified economic sanctions. As we express our commonly felt desire for the removal of these sanctions against our country, I urge you all to be a mindful of maintaining peace, law and order.
"Buses will be available at usual pick up points from 6am. The march will commence at the Robert Mugabe Square to the National Sports Stadium where solidarity messages will be delivered.
"Let us come out in large numbers to show the world that Zimbabwe is a free, democratic and peace loving nation which needs everyone's support as we strive for our economic emancipation," he added.
Sanctions, he said, have also prevented the creation of mutually beneficial investment relations with countries that have imposed sanctions on Zimbabwe.
In Matabeleland South, the anti-sanctions march in Beitbridge will be led by Zanu-PF's Secretary for Administration Dr Obert Mpofu and ANC secretary-general Cde Ace Magashule of South Africa).
Proceeding are expected to start at 7am at the District Development Coordinator's (formerly District Administrator) offices and the procession will go through the Beitbridge Border Post, along the Beitbridge-Bulawayo highway and end at Dulivhadzimu Stadium.
Organisers of the event said yesterday that they had covered a lot of ground in terms of logistics.
Beitbridge District Development Coordinator (DDC) Ms Skhangazile Mafu said people were encouraged to attend the anti-sanctions march in their numbers.
"This is a pure Government programme and we discourage people from wearing political regalia. Our teams are busy mobilising people from the nearby villages including Dumba, Mawale, Makakavhule, Mtetengwe, Chamnanga, Lutumba, Nuli and Tshapfuche among others to take part in the event.
"We expect the march to be a very big success".
In Manicaland, Zanu-PF provincial chairman Cde Mike Madiro said they had mobilised thousands to converge at Sakubva Stadium.
"We are more than ready for the anti-sanctions march. All the seven administrative district centres are also more than ready and are very enthusiastic. They want to show their displeasure of the continuation of the illegal sanctions. The event will be overwhelmingly subscribed," said Cde Madiro.
In the Midlands, Minister of State Larry Mavima said more than 20 000 people are expected to converge in Gweru for the anti-sanctions march.
The procession will start at the traffic circle along Bulawayo Road and people will march up to the Boogie Tour along Main Street where solidarity speeches will be delivered by captains of industry, civil society organisations, students, small to medium enterprises, freedom fighters among others.
"We are happy that the preparations for the anti-sanctions march were successful and we are ready. We are marching from the traffic circle along Bulawayo road to an area near Kudzanayi long distance bus terminus," he said.
In Mashonaland West province all the seven districts were yesterday busy mobilising people to participate in the anti-sanctions march in Harare. By yesterday afternoon, final logistics including distribution of fuel to allow people to go to Harare were being finalised.
Mashonaland West Provincial Affairs Minister Mary Mliswa-Chikoka said it was all systems go as more than 30 buses will ferry people to Harare for the march.
"Our people have been burdened by sanctions for about 20 years meaning that some were born and have not enjoyed a stable economy because of the sanctions. We need a break and a chance as Zimbabwe to build our economy," she said.
Minister of State for Mashonaland Central Provincial Affairs and Devolution, Minister Monica Mavhunga said it was all systems go for today's anti-sanctions march in the province.
Addressing the media at her offices in Bindura yesterday afternoon, she said they had mobilised enough transport for the 33 pick-up points in Bindura and Shamva where people will be picked up for the provincial programme to be held at Chipadze Stadium.
"We expect a bumper crowd to converge for the provincial march. Mazowe District will represent the province at the national event in Harare. There are also several district centres where the marches will be held.
"We appreciate the support we received from the corporate world to beef up what Government has availed."
She said the programme starts at 8am with people marching from Shamva-Chipadze Turn-off, Bindura Showgrounds and Bindura Country Club respectively and converge at NSSA Complex before proceeding to Chipadze Stadium for the provincial event.


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text:
\section{Introduction}

Traditionally,  planetary habitable zones are defined as the range of distances from a star within which a planet can orbit such  that  stellar luminosity heats the planet to a temperature range that can sustain gravitationally bound liquid water \citep{Huang1960,Kasting1993}.  However, even if  liquid water is essential,  the potentially catastrophic effect of stellar activity  from ultraviolet and X-ray photons, and   stellar winds on the planetary atmosphere must also be
considered \citep[e.g.][]{Lammer2013}. High energy photons can  photo-dissociate molecules and/or  heat atoms such that  that the atmospheric constituents exceed the escape speed at the exobase  and are catastrophically lost.
 Complementarily, a  strong stellar wind can exchange momentum with the planetary atmosphere and directly or indirectly eject the essential constituents.

 The overall effects of stellar activity on atmospheres are commonly
(if not misleadingly) delineated as ``thermal" or ``non-thermal" mechanisms
 \citep[e.g.][]{Hunten1982,Kumar1983+,Kasting1983+,Shizgal1996+,Lammer1991+,Hunten1993,Seager2010,Lammer2013}.  For the former,  energy is primarily absorbed and converted to thermal energy.

 The potential for ejection amounts to a comparison between thermal velocities and escape speed.
Non-thermal mechanisms refer to those in which the input energy is not thermalized by collisions and/or may involve a change of chemistry  or ionization  state of the influenced particles.   Erosion of atmospheres by  stellar winds is an important example of the latter,
and the focus of the present paper.  Ultimately, a  realistic determination of habitability will depend  on understanding the high energy coronal activity from stars and the efficacy with which  planetary atmospheres are protected against the associated radiation and winds.

 The magnetic field strength and X-ray activity of solar-like stars
increase with rotation rate for slow rotators and
then saturate for very fast rotators \citep{Noyes1984,Schrijver2000,Pizzolato2003,Mamajek2008,Wright2011,Vidotto2014, Reiners2014}.

 Relationships between stellar activity, rotation, and magnetic field strength are all connected   to the dynamo origin of these fields within the stars; it is an ongoing enterprise  of research to understand these connections and make them quantitative \citep{Karak2014,Kitchatinov2015,Sood2016,Blackman2016}.
In the absence of significant cooling, the winds from solar-like stars, which also draw from the coronal magnetic and thermal energy, are also likely significantly stronger for younger stars.
 This too, however, is debated and a topic of active research  \citep{Wood2006,Wood2014,Cohen2011,Suzuki2013,Matt2015,Blackman2016}.

Planetary magnetospheres produced from core dynamos are widely perceived to be protective against erosion from stellar winds.
This is of topical interest in understanding the evolution of the early Earth \citep{Tarduno2015+} and well as the potential habitability of exoplanets \citep{Nascimento2016+}.  The  planetary magnetic field  acts as a magnetic cage that tempers stripping by stellar winds, redirecting  flow  starting at a bow shock, and  diverting it around  the planet. The bow shock lies just outside the radius of the ``obstacle" namely the magnetopause, where the ram pressure of the stellar wind is balanced by the magnetospheric pressure of the planetary atmosphere. For example, the difference between the current water inventory of Earth versus that of  Mars has long been  thought to be due to the presence of an internally generated magnetic field on the   former, and the loss of water on the latter \citep[e.g.][]{Luhmann1992+,Lundin2007}.

However, some observations have also led to  speculation that the  magnetosphere might not be exclusively protective  \citep{Brain2013}.
For example,
the present-day total atmospheric ion escape from Earth, Mars and Venus appears to be within similar orders of magnitude, at 10$^{24}$-10$^{26}$ ions s$^{-1}$
\citep{Barabash2010, Strangeway2010, Dubinin2011+,Wei2012,Jakosky2015+,Strangeway2017+},  but here too there is debate fueled by the limitations of observations and models.  Because Earth has an internal geomagnetic field and Mars and Venus do not,  the role of the internal magnetic field might seem to be  un-influential.
 Note that understanding the  present kinematic loss rates
and the  role of the magnetic field does not by itself
determine  relative habitability. The latter also depends on the long term
history of each planetary atmosphere  that includes its chemistry  and in particular, water loss \citep{Tarduno2014}, which is crucial for life.

The competing  influences of planetary magnetic fields are also manifest in their role of channeling ions.
Incoming  ions are channeled toward the poles in a large scale dipole configuration. In this respect,  magnetic fields might exacerbate atmospheric loss rather than abate it \citep{Brain2013}.   Such an effect would preferentially
eject heavy ions that would otherwise be gravitationally bound at atmospheric temperatures, unlike light ions like
H$^{+}$ whose thermal speed would  already exceed  the escape speed.
Supporting evidence comes from
observations  \citep{Strangeway2005}
  showing an enhanced  outward  oxygen ion flux from auroral zones  consistent with
  a two order-of-magnitude concentration of  solar wind energy     \citep{Moore2010}.

On the other hand, dipole magnetic fields
can also recapture at least some of this outgoing flux. For example, \cite{Seki2001} conclude that the polar outflow of O$^{+}$ from Earth today is some 9 times greater than the net loss, considering recapture in the magnetosphere.  A local outflow might therefore not always result in a catastrophic global outflow.  Complementarily, the depth to which incoming ions can penetrate also depends on competing forces such  as a magnetic mirror force
 \citep{Cowley1990+}.

Despite  the complexities that determine the actual fate and influence of the incoming particle flux, the associated gain in energy and momentum of the  atmosphere cannot
exceed that supplied by the  wind.
This in turn leads to  an approximate upper limit on the potential atmospheric mass  loss (as we shall see) if the energy or momentum conversion into escaping particles were maximally efficient and the atmospheric  particles were not already hovering close to the escape speed before the influence of the wind.  It is both instructive, and important even, to constrain how an internally produced magnetic field affects this approximate upper limit compared to a planet without an internal magnetic field. As we will see, even this simple comparison provides some conceptual and quantitative insight.

In section 2 we estimate   wind  mass and energy  supply rates entering  planetary atmospheres for ``magnetized" vs. ``unmagnetized" planets (with these terms to be defined more carefully therein).  We  take into account magnetic reconnection when the stellar wind field is anti-aligned with the planetary field and quantify the competing effects of reduced inflow speed and increased collection area. We also include the effects of polar focusing.
In section 3, we use  the results of section 2   to derive approximate upper limits on the mass loss rates for magnetized vs. unmagnetized planets,  and include estimates for both energy and momentum-limited loss rates.
In section 4 we  apply the results to Earth, Mars, and Venus. Using time-evolution models for the host stellar wind ram pressure to calculate the time-dependent magnetospheric stand-off distance, we show how  the solar wind mass  capture rates throughout Earth's history are actually larger  than those for an unmagnetized Earth-like planet with a small ionosophere, even though total maximum energy capture rates, and the associated  atmospheric mass loss rates would be lower.
This conclusion changes for Earth's future when polar focusing is included.
By  consideration of  momentum transfer from wind to the  atmosphere-- and
specifically to pick-up ions for Venus and Mars-- we predict $O^+$ loss rates of Mars, Venus and Earth  from
our formalism. We  conclude in section 5.

\section{ Mass and Energy Loading With and Without A Magnetosphere}
\label{sec2}

\subsection{Standoff distance for planet with dipole field}

For a  planet with a dipole  magnetic field and a stellar wind dominated by  ram pressure,  the standoff distance $d_s=r_s$, where the $r_s$ is determined by
where the magnetic pressure of the planet equals the ram pressure of the impinging stellar wind, and
is given by
\begin{equation}
{r_s^3\over r_p^3} = \left({B_p^2 \over 8\pi\rho_w v_w^2}\right)^{1/2},
\label{4.4.5}
\end{equation}
where $r_p$ is the radius of the planet, $B_p$ is the magnetic field strength at the planetary surface, $\rho_w$ and $v_w$ are the stellar wind density and speed at $r_s$ respectively.

\subsection{Incoming mass flux for intrinsically ``unmagnetized" and ``magnetized" planets}
The rate of   stellar wind ions entering a  planet's atmosphere depends on the product of the effective area onto which ions are captured and
the speed of the inflow.
We focus  on comparing planets of two extremes which we delineate   as ``magnetized" and ``unmagnetized". The difference is shown schematically in Figure \ref{schematic},
where the two  cases  are superimposed.
For present purposes, ``magnetized" planets  are those
for which the standoff distance is determined by a  magnetopause of radius $r_s >> r_p$.
The thick lines of Fig. \ref{schematic} correspond to this case;  the incoming flow is represented by the black lines and the outgoing mixture of  wind and atmosphere  flow is given by thick blue lines. The cross section for interaction is given by the dotted black line.
  an
Complementarily,  our ``unmagnetized" case  refers to planets whose standoff
distance $d_s$ from the incoming wind ram pressure equals the radius $r_i$ set by  ionospheric plus induced magnetic pressure.  The  cross section of interaction  between the stellar wind   and the atmosphere is, however, determined by an interaction radius $r_T\ge r_i$
which  we write as
 \begin{equation}
  r_T=r_i+ r_g
  \label{rT}
  \end{equation}
   where  $r_g$  is the gyro-radius of the
  atmospheric  ions, an upper limit of which is that for
  the uncompressed wind magnetic field at the planet.

  The thin lines of Fig. \ref{schematic} capture this schematically.
  The incoming wind flow arrows are red and the mix of wind and outgoing atmospheric ion flow arrows are purple.
  The green represents  $r_g$ at the terminator such that the cross section of interaction is given  by the red dotted line.   For  Mars and Venus, the ionopause and magnetopause (i.e., the induced magnetopause boundary) are just  a few hundred km above the surface,  and not dramatically delocalized from the exobase radius \citep{Russell2016+}.
  For oxygen ions, $r_g$ can be
  comparable to, or even significantly larger than the planet radius (particularly for Mars) as we   discuss  further in section 4.2.2.
For a more compact case, it is possible that  $(r_i+r_g)-r_p < r_p$ such that
  $r_T \sim r_p$.  This does not preclude the planet from still having  a non-trivial atmosphere.

For our ``unmagnetized" case then, the incoming mass per unit time potentially influencing  the cross section determined by $r_T$ is given by
\begin{equation}
{\dot M}_{c}\simeq \frac{\pi r_T^2}{4\pi R^2}{{\dot M}_w},
\label{4.4.1}
\end{equation}
where ${\dot M}_w$ is the star's mass loss rate per unit time of the wind,
 and  $R$ is the planet-star distance.

 In contrast, for the ``magnetized" case, we consider particle capture by the magnetosphere to occur primarily during reconnection events between the stellar wind is fand the  planetary magnetosphere. This is because  we are considering  the magnetized case to have a magnetopause so far from the exobase  that the atmospheric density is
too low for interacting in that region to cause significant atmospheric mass loss. The reconnection
allows the wind plasma closer access to the atmosphere.  Other pathways to particle capture such as Kelvin-Helmholtz mixing or impulsive penetration  can also occur \citep{Gunell2012}, but we  focus on magnetic reconnection as the primary facilitator.

 \cite{Paschmann2013} point out that about 50\% of the time
reconnection is favorable at the Earth's magnetopause.  This is not  directly attributable  to the fact that  after averaging over  many rotations and  cycle periods over which the field periodically reverses,  the shear angle between the wind field and magnetospheric field would be  favorable  to reconnection
approximately half of the time. Rather, the favorability depends on a  combination of shear angle, current sheet thickness, and variation  in the plasma $\beta$ (ratio of plasma to magnetic pressure) across the magnetopause.  Reconnection is still possible with small shear angles (and thus strong guide field) but requires more symmetry in $\beta$ across the magnetopause interface  than the large shear angle cases.    In this respect,
there need  not be a strict correlation between mass loading and field orientation of the solar wind.

During  the  reconnection phase, the effective mass capture area for stellar wind ions can approach the  magnetopause cross section (on the dayside).
Determining the overall efficacy of the magnetosphere at keeping incident wind particles out then requires accounting for the competing effects of the increased  collection area with the reduced speed.  With this in mind, the mass  collected  per unit time ${\dot M}_{c,m}$ is given by
\begin{equation}
{\dot M}_{c,m}= \frac{\pi r_{s}^2 }{4\pi R^2 } \frac{v_{in}} {v_w}{{\dot M}_w\over 2}
\label{4.4.2},
\end{equation}
where
$v_{in}$ is the effective inflow speed, taken to be  the reconnection speed $v_{rec}$ derived below.

The factor of  ${{\dot M}_w\over 2} $
 accounts for the fact that the incoming wind loads into the atmosphere only when there is reconnection.

The ratio of the mass per unit time captured by a planet with a magnetosphere to that captured by the  same planet without a magnetosphere is given by the ratio of Eq. (\ref{4.4.2}) to Eq.  (\ref{4.4.1}). This is
\begin{equation}
Q\equiv{{\dot M}_{c,m}\over {\dot M}_{c}}= {1\over 2} \left(r_s\over r_T \right)^2 \left(v_{in}\over v_w\right).
\label{4.4.3}
\end{equation}
Not all of the variables in Eq. (\ref{4.4.3}) are independent, but we can simplify crudely as follows:
reconnection  at the standoff point  is generally   asymmetric  across the current sheet and
the  incoming speed of reconnection
from the wind-side toward the  sheet is given by \citep{Cassak2007+}
\begin{equation}
\begin{array}{r}
v_{in}=v_{rec}\sim2 { \tilde \chi}\left({B_{w}B_2^{3} \over4\pi (B_w+B_2) (B_w\rho_2+B_2\rho_w) } \right)^{1/2},
\end{array}
\label{4.4.4b}
\end{equation}
where $B_w$ is \textbf{the} field on the wind-side of the magnetopause, $B_2$ is the planet field on the
magnetospheric side of the reconnection region, and ${ \tilde\chi}$ is the ratio of current sheet thickness to length.
 For Earth at least,   data suggest  $B_2 >B_w$ and $B_2\rho_w> B_1\rho_2$ \citep{Sonnerup2016} so
$v_{in} $  reduces to
\begin{equation}
\begin{array}{r}
v_{in}=v_{rec}\sim {2 B_{w}^{1/2}B_2^{1/2} \over (4\pi\rho_w)^{1/2} }{\tilde \chi}
 \simeq \chi
\left({B_p \over \sqrt {4\pi \rho_w }}\right)
\left({r_p \over r_s}\right)^3,
\end{array}
\label{4.4.4}
\end{equation}
where $\chi=2{\tilde \chi}\sqrt{ B_w/B_2}$, and we use the dipole
scaling $B_2 = B_p ({r_p / r_s})^3$ where $B_p$ is the surface field strength.
 Observations and simulations are roughly consistent  with $\tilde \chi =0.1$   \citep{Cassak2007+}
 and in turn $0.5\ge \chi\ge 0.1$.

We now combine Eqs.  (\ref{4.4.4}) and (\ref{4.4.5})  with Eq. (\ref{4.4.3})
for the specific case in which $r_T \sim r_p$, the unmagnetized case with a compact atmosphere.
The result is
\begin{equation}
v_{in}/v_w ={ \chi} {\sqrt 2},
\label{vrecvin}
\end{equation}
and
\begin{equation}
Q={\chi\over \sqrt 2} (r_s^2/r_p^2)
=7.07
\left ({\chi\over 0.1}\right)  \left({r_s/ r_p \over 10}\right)^2,
\label{4.4.5a}
\end{equation}
where we have scaled to present day Earth-like values of $\chi$ and $r_s/r_p$.
That $Q$  can exceed  unity  highlights the important effect  of the increased collecting area that  the magnetosphere provides.
 Eq. (\ref{4.4.5a}) shows that the weaker the wind, the higher the rate of mass capture for a magnetized planet relative to an  unmagnetized planet since $r_s/r_p$  increases for weaker stellar winds.  In what follows, we assume  $\chi$ to be relatively constant over the range of $r_s/r_p$
 calculated. This is consistent with our assumption  that
 the current sheet geometry is  relatively constant and the fact that
 $\xi$ depends on the ratio of   $B_w$ to $B_2$.  Both of these two field strengths are likely larger for younger stars; $B_w$ is correlated with the surface field which is stronger for younger stars with higher coronal thermal power for the wind.  The wind's thermal
 energy    supplies its ram pressure which, in turn, reduces $r_s$ and increases $B_2.$.

  \begin{figure}
\centering
{
\includegraphics[width=1\columnwidth]
{schematicfigure}}
\caption{Schematic of both ``magnetized" and ``unmagnetized" cases superimposed with the same sized planet for comparison.
[Adapted into a composite from Dubinin et al (2011) and public domain graphic by A. Krasse (NASA Goddard)]. Stellar wind is incoming from the left.
{\it For the "magnetized" planet case, focus on  the thick black, pink, and blue lines and arrows and ignore the thin lines:} the thick pink lines are the magnetic field of the planet;  the thick black arrows indicate incoming solar wind flow; the thick  blue arrows indicate the outgoing flow from the atmosphere, so colored to indicate that they may also include  solar wind material.
The projected cross section of the magnetopause/interaction ($\sim \pi r_s^2$, where $r_s$ is defined in  Eq. \ref{4.4.5})  is indicated by the thick vertical dotted black line at the left. The outer bubble is the bow shock and the white lines are the interplanetary field.
{\it  For the "unmagnetized" case, focus on the thin lines and arrows and ignore the aforementioned thick lines:}   the thin curved dotted line is the bow shock;  the inner dotted line is the boundary of the induced magnetopause and the thin solid line between those two bounds the the region
 where pickup ions interact with the incoming flow.
 The red arrows indicate the incoming flow and the violet arrows indicate
 the pickup ion flow swept by the stellar wind.
 The  green distance between the ionopause and  the bow shock can  be of order a gyro-radius away of thermal ions, and increases away  from the dayside ionopause  as the flux pile up decreases and the field weakens to its ambient value.
 The projected cross section  of the magnetopause/interaction area for this "unmagnetized" case ($\sim \pi r_T^2$, see Eq. \ref{rT}),
  is indicated by the dotted vertical red line.}
 \label{schematic}
\end{figure}

 \begin{figure}
\centering
\vskip-0.2in
{\includegraphics[angle=-90,width=1\columnwidth]
{Fig2a9-18}
\vskip-0.4in
\includegraphics[width=0.9\columnwidth]
{Fig2b9-18}}
\caption{
Standoff distance in units of Earth-like planet radius vs.  age for different planet dipole moments  and   different wind evolution models:  top  \citep{Blackman2016};
bottom figure adapted from \citep{Tarduno2010}.
Green  lines of both panels  represent models  whose endpoint matches present day measurements.  Solar wind model curves in  bottom  panel result from combining mass-loss  to X-ray flux correlation with X-ray flux to age correlation (see text).

Magnetic dipole data sources for bottom panel are as follows: Karelia  \citep{Smirnov2003}, KVP, DP (Kaapvaal Pluton, Dalmien Pluton respectively) \citep{Tarduno2007}, and BGB, NGB (Barberton Greenstone Belt, Nondweni Greenstone Belt) \citep{Tarduno2010}.
The geodynamo may have started shortly after the lunar forming event, when core chemical stratification was disrupted
\citep[e.g.][]{Jacobson2017}.
 In both panels:    solid orange and solid black lines are   thresholds of  $r_s/r_p$  above which  mass   (Eq. (\ref{4.4.6}))
   and energy   (Eq. (\ref{en15a})),  respectively, per  solid angle captured toward the poles are higher  for a magnetized planet.  Dashed orange and dashed black lines are  the
   corresponding thresholds
   for total wind mass (Eq. (\ref{4.4.5a})) and energy  (Eq. (\ref{en15}))
   respectively.

   Dashed black is absent on bottom panel due to the smaller  ordinate range.}

 \label{standoff}
\end{figure}

\subsection{Focusing toward the polar caps}

Magnetic polar caps subtend a solid angle  no larger than that of a hemisphere (2$\pi$)  and could be much less, as in the case of Earth.
When  captured particles funnel  toward  polar caps along the magnetic field rather than being uniformly distributed over a hemisphere,  the associated local
mass flux  (mass per unit time per area) and energy flux within the cap solid angle
is  enhanced by  a  factor  $1/f_c$, where
\begin{equation}
f_{c}= (1-cos \theta_c)\le 1
\label{fc}
\end{equation}
is the areal fraction of a hemisphere
subtended by a polar cap of colatitude  $\theta_c$.

If we restrict ourselves to  the case when the incoming wind flow is perpendicular to the planet's magnetic dipole axis, we can then estimate $\theta_c$ for a dipole from
the equation for the local  polar geometry of field lines, namely
 \citep{Russell2016+}
  \begin{equation}
r{ d\theta \over dr} = {B_\theta\over B_r}.
 \label{d1}
\end{equation}
For a vector dipole field in spherical coordinates of magnetic moment $\bf m$
\begin{equation}
{\displaystyle \mathbf {B} ({\mathbf {r} })={\frac {|\mathbf {m} |}{|\mathbf {r} |^{3}}}\left(2\cos \theta \, \mathbf {\hat {r}} +\sin \theta \,{\boldmath {\hat {\theta }}}\right)},
\end{equation}
from which the  ratio of the two field components is
\begin{equation}
{B_\theta\over B_r}={tan\theta\over 2}.
 \label{d2}
\end{equation}
Using Eq. (\ref{d2}) in  Eq. (\ref{d1})  and integrating
gives
\begin{equation}
r=r_e sin^2\theta,
\label{theta}
\end{equation}
 where $r_e$ is the value of $r$ at which a particular field line crosses the equator $(\theta=\pi/2)$.
The  value $\theta=\theta_c$   is determined by setting $r_e=r_s$, the magnetopause radius,
and $r=r_p$ because  the field lines  anchored on the two polar circles $\theta = \theta_c$ at  $r=r_p$
represent the anchor loci of the  closed field lines
just at the inner edge of the magnetopause.
Field lines anchored with  $\theta\le \theta_c$ extend into the wind-side of the magnetopause, along which wind plasma can only enter during reconnection.

Using the aforementioned substitutions  in Eq. (\ref{theta}) along with Eq. (\ref{fc}) gives
\begin{equation}
f_c=1-\sqrt{1-r_p/r_s}.
\label{fc2}
\end{equation}
For a fixed wind mass flux, decreasing the magnetic field   increases
$r_p/r_s$, thereby decreasing  $f_c$.
Correspondingly,  for a  fixed planetary magnetic   field, $f_c$  decreases
with increasing wind ram pressure. This implies that
  $f_c$ would generally increase with stellar age (as wind power weakens) for steady planetary field strengths.

We  define $q\equiv Q/f_c$ as the ratio  of mass
capture rate per solid angle by a magnetized planet that includes polar cap channeling to
that in the absence of a magnetosphere altogether.
From  Eq. (\ref{4.4.5a})  we then obtain
\begin{equation}
q
\simeq  {Q\over f_{c}}
\simeq 70.7\left({{\chi}\over 0.1}\right) \left({r_s\over 10r_p}\right)^{3}
\left[1+\left( 1-{r_p \over r_s}\right)^{1/2}\right],
\label{4.4.6}
\end{equation}
where the factor in square brackets ranges  between 1 and 2.
Note that
 $q/Q=1/f_c$, which  increases with stellar youth.

Taken at face value,  Eqs. (\ref{4.4.5a}) and  (\ref{4.4.6})
 highlight that  the  mass   captured by a  magnetized Earth-like planet, when averaged over many  wind field reversals could  be  greater than without a magnetic field.
{Our analysis here supersedes that of \cite{Tarduno2014}
where we did not give explicit expressions for the reconnection speed and polar focusing
or emphasize that
$Q$ and $q$ can exceed unity while the analogous energy
rate ratio can still be much less than unity. }

\subsection{Incoming energy flux with and without a magnetosphere}

The  ratio of energy input rates
 imparted to the atmosphere  for magnetized vs. unmagnetized planets
can be obtained by multiplying  Eq. (\ref{4.4.5a}) and Eq.  (\ref{4.4.6})
 by

\begin{equation}
\xi={ \left({c_s^2\over \Gamma-1}+v_{in}^2\right)\over \left({c_s^2\over \Gamma-1}+v_{w}^2\right)}={ \left({c_s^2/v_w^2 \over \Gamma-1}+2{\chi}^2\right)\over \left({c_s^2/v_w^2\over \Gamma-1}+1\right)},
\label{enflux}
\end{equation}
where $c_s$
 is the incoming sound speed and $\Gamma$ is the adiabatic index.
The energy flux includes contributions from the enthalpy and the
bulk kinetic energy of the incoming material  with sound speed $c_s$.

Multiplying  Eq. (\ref{4.4.5a}) and Eq.  (\ref{4.4.6}) by  Eq. (\ref{enflux}) then gives
   the ratios of energy capture rates of the magnetized to unmagnetized planet for unfocused
   and polar focused cases  as
 \begin{equation}
 Q_{en}\sim0.21\left({\xi\over 0.03}\right)\left({\chi\over 0.1}\right)
 \left({r_s/r_p\over 10}\right)^2,
 \label{en15}
 \end{equation}

 and
  \begin{equation}
  \begin{array}{l}
 q_{en}={Q_{en}\over f_c}\\\simeq 2.12 \left({\xi\over 0.03}\right) \left({\chi\over 0.1}\right)
 \left({r_s\over 10r_p}\right)^{3}
\left[1+\left( 1-{r_p \over r_s}\right)^{1/2}\right],
\end{array}
  \label{en15a}
 \end{equation}

respectively.
The scaling  of $\xi =0.03$ arises if we use fiducial values for the  incoming wind of
$c_s\simeq 3.9\times 10^6$cm/s (corresponding to $T\simeq 10^5$K),
$v_w=400{\rm km/s}$, and $\Gamma=5/3$.
 Eq. (\ref{en15})  shows that  the total energy collected by

 a magnetized  planet scaled to present day Earth-sun-like parameters is  less than that of the magnetized planet. However  Eq. (\ref{en15a}) shows that the polar energy flux concentration
can be comparable, or even greater for the magnetized planet.

\section{Limits on Mass Loss Rates from Energy and Momentum Conservation}
\label{sec3}

The exact determination of the induced mass loss from an  incoming stellar wind
depends upon detailed plasma and chemical properties that determine how the incoming energy and momentum  is converted to outgoing particles \citep{Sibeck1999,Lammer2013,Russell2016+}. We re-emphasize here that we are considering atmospheric mass loss estimates that involve the wind
 and not those arising only from  radiative forcing. The latter is needed to produce ions,
 but  atmospheric mass loss direct from only radiation  without the influence of the stellar wind  is    insufficient to explain the full history of mass loss
for Earth and Venus, and even Mars \citep{Dubinin2011+,Dong2018b+}.

 The extent to which an intrinsic planetary field can trap
 outgoing particles  can also limit the otherwise induced  loss.
But regardless of  how the energy and momentum inputs are subsequently converted into outgoing particles,
we can  compare estimates of  approximate maximum atmospheric mass loss rates  (``approximate" is explained below)  that the wind could induce  for  magnetized and unmagnetized cases.
The distinction between  these two cases is essential when the exobase is below the magnetopause or ionopause.

 The wind energy flux times the capture area for inflow speed $v_{in}$ is given by
\begin{equation}
\rho_{in} Av_{in}\left({c_s^2\over \Gamma-1}+v_{in}^2\right)={\dot M}_{in} \left({c_s^2\over \Gamma-1}+v_{in}^2\right),
\end{equation}
and the wind momentum flux  times the capture area is
\begin{equation}
\rho_{in}A \left( v_{in}^2+{c_s^2\over \Gamma}\right)={\dot M}_{in}v_{in} \left(1+{c_s^2\over \Gamma v_{in}^2}\right).
\end{equation}

The maximum  outflow induced mass loss rate   corresponds to the case in which all of  the incoming momentum or energy gets converted into outflow with  outflowing ions moving just  at the escape speed $v_{esc}$
along open field lines. For   thermal, isotropically  distributed ions,   the relevant
initial  ion speed would be the most probable particle speed at the exobase $v_p$.  If
$v_p$  were already even as high as a fraction  $\lambda=1/4$ of the escape speed $v_{esc}$ before any wind influence, then for a  Maxwellian  distribution $f(v)=({-mv^2\over2\pi kT})^{3/2}e^{-mv^2\over2 kT}$,
only a fraction
${\int_{ v_{p}/\lambda}^{\infty}  f(v) v^2 dv\over  \int_{0}^{\infty}  f(v) v^2 dv} \sim 7.4 \times 10^{-9}$
would be above the escape speed, and the fraction  drops exponentially with decreasing $\beta$.
When this fraction times the atmospheric density at the exobase is less than that of the stellar wind,
 the number of particles above the escape speed would be negligible.

But even particles  with  speeds   as high as $v_{esc}/4$, have only 1/16th of the escape energy.  Therefore, assuming that particles start from zero energy does not lead
to a significant difference in estimating  a mass loss rate.
Moreover, for cases when the particle gyro-radii are initially much  smaller than the planet scale,  then only motion along open field lines  leads to escape. Since the escape path  is locally   along 1 direction,  no more than 1/3 of the particles   escape when the most probable speed reaches the escape speed for an isotropic distribution.  To ensure that all particles   escape if they were initially at $1/16$ the escape energy then requires  $3-1/16\sim 3$ times the escape energy to be imparted from the incoming wind.

If the ratio of the inflow speed to the escape speed exceeds unity, then energy conservation gives a larger outflow mass loss rate limit than momentum conservation.
 Otherwise, momentum conservation determines the larger mass loss rate limit.
For a steady state,   the corresponding energy and momentum rate balance equations
for inflow and outflow are given respectively by
\begin{equation}
{\dot M}_{in} \left({c_s^2\over \Gamma-1}+v_{in}^2\right)
=
  {\dot M}_{out} v_{esc}^2,

 \label{enint}
\end{equation}
and
\begin{equation}
{\dot M}_{in}v_{in} \left(1+{c_s^2\over \Gamma v_{in}^2}\right)
=
{\dot M}_{out} v_{esc}.
 \label{momint}
\end{equation}
By rearranging  each of Eq. (\ref{enint}) and  (\ref{momint})
 to obtain an expression for
 ${\dot M}_{out}$, we can combine
 the results to express  the maximum of the two upper limit estimates for the outflow mass loss. If we also allow for the polar focusing fraction $f_c$, the combined result is
  \begin{equation}
  \begin{array}{l}
{ {\dot M}_{out,max}\over {{\dot M}_{in}}}\\
={1\over f_c} {v_{in}\over v_{esc}}\left[{{v_{in}\over v_{esc}}\left(1+{c_s^2/v_{in}^2\over \Gamma-1}\right)}, \left(1+{c_s^2/v_{in}^2\over \Gamma }\right)\right],
\end{array}
\label{outboth}
 \end{equation}
 where the first term in brackets is the result from energy conservation and the second term is from momentum conservation. The former dominates when $v_{in}> v_{esc}$, and the latter when
 $v_{in}< v_{esc}$. If all the energy and momentum instead went into  particles
 moving at some speed $v_{ave}> v_{esc}$, then $v_{ave}$ would replace $v_{esc}$ in
 Eq.   (\ref{outboth}) and the mass outflow rate estimate would be correspondingly reduced.

 \section{Implications for Atmosphere Protection}
 \label{sec4}
We now apply the formalism of the previous
sections to the time evolution  of magnetospheric protection for the
Earth-sun system, and to the  separate question of present day oxygen ion
loss rates from Earth, Mars, and Venus.

\subsection{Influence of  stellar activity variation on  protection by an Earth-like magnetosphere}

The blue curves of the top panel and the red curves of the bottom panel of Fig. \ref{standoff} show the time evolution of $r_s/r_p$ for different values of the planetary magnetic field (assumed to be constant for each curve) for an Earth-like planet at 1AU from a sun-like star. The top panel uses the minimalist, but holistic theoretical model of \citep{Blackman2016} to compute the standoff distance from the  wind ram pressure. The latter is  derived from the time evolution of magnetic field, rotation, mass loss, and X-ray luminosity predicted from the physics of the model.
Although the correlation between  X-ray luminosity and stellar mass loss has been questioned \citep{Cohen2011}, this query is based on short-term observations of the Sun that may not apply to the billion year time scales of interest. The bottom panel in Fig. \ref{standoff} shows curves from \cite{Tarduno2010} which utilize the empirical mass loss values for solar-like stars from  \citep{Wood2006} based on H I Lyman-$\alpha$ data. Those values are observed to correlate with X-ray flux, which in turn was used to empirically determine stellar ages.
 The magnetopause standoff distances are truncated at 700 my because the few available young stellar analogs hint at lower rates of mass loss \citep{Wood2014}, breaking the correlation.
(The saturation of X-ray flux with youth also  makes
age determination more difficult for younger stars \citep{Mamajek2008,Wright2011}.)

The green curve in the top panel of  Fig. \ref{standoff}  corresponds to the case that matches  present day field measurements, as also  labeled on the bottom panel.
The curves of both panels show that  $r_s/r_p$ decreases with youth
because of the stronger ram pressure of the solar wind, while the planetary field remains nearly constant.
The horizontal lines in the two panels of Fig \ref{standoff} correspond to the specific thresholds calculated in Section {\ref{sec2}.
Namely,  the orange solid lines  show the threshold of $r_s/r_p$
above which  $q\ge 1$ from Eq. ({\ref{4.4.6}) (assuming the lower limit of $1$ for the  square bracketed quantity).
 The orange dashed lines show  the  threshold above which $Q\ge 1$ from  Eq. (\ref{4.4.5a}).
These are, respectively, the thresholds above which the polar and total atmospheric mass collection rates for the magnetized planet exceed those for the unmagnetized planet with a compact atmosphere.
The  solid and dashed black curves, which correspond
to Eqs  (\ref{en15a}) with the  square bracketed quantity equal  to $1$,
and (\ref{en15}) respectively,
 indicate the threshold ratio of $r_s/r_p$
above which the polar focused and total energy  capture rates by the magnetized planet exceed that for  an unmagnetized
planet.  Because energy conservation rather than momentum conservation determines the  larger of the two values on the right of  Eq. (\ref{outboth}) for Earth-sun-like
systems, these curves also indicate the corresponding thresholds above which the magnetized planet  has  higher upper limits on mass loss from stellar-wind atmosphere erosion as compared to the unmagnetized planet.

Given the fiducial parameter values used to make the horizontal lines,
both panels of Fig. \ref{standoff}  reinforce the same  implications:
for most of  an Earth-like planet's history,  more total mass and  polar mass flux can be captured by the magnetized planet than for  the correspondingly unmagnetized planet, even though  less total energy is captured by the magnetized planet over its past history.  As shown,  this circumstance will also persist for the the long term future.

Since the maximum mass outflow rate for an Earth-sun-like system is determined by energy rather than momentum in Eqn. (\ref{outboth}),  this  further implies that the upper limit on  the mass loss rate would be reduced by a magnetosphere throughout the  Earth-like planet's past and future.

 If we include polar focusing using $f_c$ from Eq. (\ref{fc}) however, the solid black horizontal lines of Fig \ref{standoff} exemplify that  the polar  focused  energy flux (and thus the resulting upper limit on  atmospheric mass outflow
from Eq. (\ref{outboth}))
 can be {\it higher} in the recent past and future  for the magnetized Earth compared to an  unmagnetized Earth.
Here the two panels differ somewhat in where the line crosses the
standoff curve that best matches present day  but as alluded to above, neither the data nor the models are   accurate enough for this time scale to be constrained to better than a factor of 2.

Irrespective of the cross-over time discussed above,
Fig. 2 shows, for an Earth-like magnetized planet, that the initial outgoing mass loss due to interaction with the wind
 (and ignoring return flow) can be larger with a magnetosphere than without under certain conditions because the magnetosphere
can capture and focus more incoming wind energy than would otherwise have access to
the atmosphere.
 How close the actual mass loss corresponds to  the maximum
 limit implied by Eq. (\ref{outboth})  depends on rate of ion return and on how incoming energy and momentum interact with specific planetary atmospheres.
 We touch on the latter in the next section.

\subsection{Partial  explanation of  Oxygen ion loss from Mars, Venus, and Earth}

The question of why $O^+, O^{+}_2$    loss rates on Earth, Mars and Venus  are apparently within a few orders of magnitude of each other is of interest. This  has led  some to question the traditionally assumed protective role of an internally generated magnetosphere \citep{Strangeway2010,Wei2012,Strangeway2017+} since Earth has one but Mars and Venus do not.
The detailed processes and local conditions of different atmospheres are time dependent, and the measured rates   depend on solar activity phase and spacecraft  location, so there is a range of more than an order of magnitude even  for a given planet.
The complexity of the underlying systems
ultimately require  combining the chemistry and microphysics to obtain detailed models.
The diversity of numerical simulations of this sort include
 M-star stellar winds interacting with habitable magnetized, and

  Venus-like planets, to obtain  standoff distances and  lower limits on mass loss
 \citep{Cohen2014,Cohen2015};

studies of the  Trappist exoplanet system \citep{Dong2018a+}; and simulations of
the time evolution of Mars' oxygen loss  \citep{Dong2018b+} that presently agrees with   recent MAVEN data \citep{Jakosky2015+}.

{ We  will use  our formalism to obtain  approximate upper limits on oxygen ion escape rates for Earth, Mars, and Venus-like planets  from  interaction with the solar wind, using energy and momentum
 conservation separately. We will  compare the results for  internally magnetized (Earth-like) and non-internally magnetized (Mars and Venus-like) cases.\bf }
 \cite{Zendejas2010+},  presented a different minimalist model  of ion outflow rates, using an imposed efficiency parameter $\alpha$ to characterize how much inflow energy is converted to outflow.    A value  $\alpha=1$ would make their results also upper limits, but they do not address the case of a magnetized planet.

We will see that the  atmospheric mass loss estimates   that result from use of momentum conservation in
our approach are in fact similar for Earth, Venus, and Mars to the level of an order of magnitude. Our limits that result from use of energy conservation are similar for the three planets to within two orders of magnitude.

\subsubsection{Upper Limits for Earth}
 To obtain an atmospheric mass loss limit ${\dot M}_{out} \le {\dot M}_{out\oplus}$
for an Earth-like magnetized planet,  we consider the fluxes as integrated over solid angle and thus  avoid $f_p$ here.
We then use Eq. (\ref{vrecvin}),
 Eq. (\ref{4.4.2}), and energy conservation in Eq. (\ref{outboth})  to obtain
\begin{equation}
\begin{array}{l}
 {\dot M}_{out\oplus}=7\times 10^4\left({\dot M_w\over 1.3 \times 10^{12}{\rm g/s}}\right)\left({v_w\over 4\times 10^7{\rm cm/s}}\right)^2\left({\chi\over 0.1}\right)^3 \\
 \left({r_s \over10  r_\oplus}\right)^2\left({R\over 1{\rm AU}}\right)^{-2}
\left({r_{ex}\over 1.2 r_\oplus}\right)\left({M_p\over M_e}\right)^{-1}\left({{{c_s^2/[2\chi^2v_w^2(\Gamma-1)]} +1}\over 1.64}\right){\rm g\over  s}.
\end{array}
\label{mdotplanet}
\end{equation}
If instead we use  momentum conservation in Eq. (\ref{outboth}),  we  obtain
\begin{equation}
\begin{array}{l}
 {\dot M}_{out\oplus}=
1.5\times 10^4\left({\dot M_w\over 1.3 \times 10^{12}{\rm g/s}}\right)\left({v_w\over 4\times 10^7{\rm cm/s}}\right)\left({\chi\over 0.1}\right)^2 \\
 \left({r_s \over10  r_\oplus}\right)^2 \left({R\over 1{\rm AU}}\right)^{-2}
\left({r_{ex}\over 1.2 r_\oplus}\right)^{1\over 2}\left({M_p\over M_e}\right)^{-{1\over 2}}\left({{{c_s^2/(2\chi^2v_w^2\Gamma)]} +1}\over 1.26}\right){\rm g\over s},
\end{array}
\label{mdotplanetmom}
\end{equation}
where  $M_p$ is the planet mass,
$r_{ex}$ is the  exobase radius, which,  along with  $r_s$ are
scaled to Earth's radius $r_\oplus$.
For Earth,   $r_{ex}\sim 1.2 r_\oplus$ and $r_s\sim 10r_\oplus$, ${\chi}=0.1$.
From Eq. (\ref{outboth}), the corresponding  particle loss rates limits from Eq. (\ref{mdotplanet}) and Eq. (\ref{mdotplanetmom}) are  respectively
\label{26}\begin{equation}
dn/dt \le  {{\dot M}_{out\oplus} \over \mu m_p}\simeq
2.62 \times 10^{27}  \left({\mu \over 16}\right)^{-1} {\rm s}^{-1},
\label{27}\end{equation}
and
\begin{equation}
dn/dt \le  {{\dot M}_{out\oplus} \over \mu m_p}\simeq
5.6 \times 10^{26}  \left({\mu \over 16}\right)^{-1} {\rm s}^{-1}.
\label{28}\end{equation}

This can be compared with
$7.2 \times 10^{25}$/s of $O^+$ observed with speeds above
escape leaving the poles, and averaged over  a solar cycle, of which 90\% seems to be   recaptured \citep{Seki2001}.

\subsubsection{Upper Limits for Venus and Mars}

For Mars and Venus,  photoionization and dissociative recombination convert  neutral molecules  into $(O^+$ or $O_2^+)$  and these collisionless ions can then be accelerated  by the motional electromotive force  \citep{Lundin+1992,Dubinin2011+,Russell2016+}  near the ionopause.
 These ions then drift perpendicular to both the incoming wind  velocity and   magnetic field.  Since the incoming flow has no initial net momentum perpendicular to the flow, lateral acceleration of oxygen ions is  accompanied by a momentum conserving flow in the opposite direction. Electrons can play this role when ion-gyro-radii are small,
but in a multi-ion-species plasma with  gyro-radii comparable or   larger than system scales,  proton streaming in the  opposite direction to the oxygen atoms  is also important
\citep{Dubinin2011+}.

As  oxygen atoms drift away from the subsolar point, their  Larmor orbits  take them into the  wind plasma where they are picked up by the oncoming wind,  accelerated and  carried past the planet.  For Venus, the ion production mechanisms likely do not  directly accelerate ions to escape speeds so the wind-atmosphere interaction is essential
but for Mars the initial energy of the ions from dissociative
recombination might produce some escape ions directly.
Photochemical dissociation may  dominate
presently,  but ion-pickup could dominate for  ancient Mars \citep{Dong2018b+}.  As  discussed in section 3, even if the ions initially have speeds as high as 1/4 the escape speed before acquiring wind energy, the  requirements to escape would  be nearly the same as if particles started from zero energy.

Focusing first on  Venus, we note that  standoff  is
determined by the ionopause particle pressure, but the induced magnetic field piles up just outside this region to a value in near equipartition with the
internal thermal pressure \citep{Russell2016+}.
The induced magnetopause boundary  is of order $50$ km or so above the  ionopause,
and the latter is  only $\sim 250$ km above the surface.
Since the ionopause, magnetopause, and exobase are all only within a few $100$ km above the surface,  they are relatively small distances above the planet radius $r_p$.  However, the influence of the wind on atmospheric mass loss requires coupling of the wind and ionosphere.
Once the ions are picked up by the wind, this coupling is determined by
finite  gyro-radii--an estimate of which will be needed to determine
 $r_T$  in the cross section for interaction between wind and atmosphere.

To quantify the atmospheric mass loss, we  first apply Eq. (\ref{4.4.1}) for ${\dot M}_{in}$  in combination with Eq. (\ref{outboth}) and $v_{in}=v_w$
to obtain $ {\dot M}_{out} \le {\dot M}_{out\venus}$. Using energy conservation  in Eq. (\ref{outboth}), we obtain
\begin{equation}
\begin{array}{l}
 {\dot M}_{out\venus}=
{1.5\times10^6}\left({\dot M_w\over 1.3 \times 10^{12}{\rm g/s}}\right)\left({v_w\over 4\times 10^7{\rm cm/s}}\right)^2
\left({R\over 0.72{\rm AU}}\right)^{-2}\\
\left({\pi r_T^2\over 8\times 10^{18}{\rm cm^2} }\right)
\left({r_{ex}\over 0.95 r_\oplus}\right)\left({M_p\over 0.81M_e}\right)^{-1}\left({{{c_s^2/[v_w^2(\Gamma-1)]} +1}\over 1.01}\right){\rm g/s}.
\end{array}
\label{mdotplanet2}
\end{equation}
If instead we use  momentum conservation in Eq. (\ref{outboth}), we obtain
\begin{equation}
\begin{array}{l}
 {\dot M}_{out\venus}=
3.86\times 10^4
\left({\dot M_w\over 1.3 \times 10^{12}{\rm g/s}}\right)\left({v_w\over 4\times 10^7{\rm cm/s}}\right)
\left({R\over 0.72{\rm AU}}\right)^{-2}\\
\left({\pi r_T^2\over 8\times 10^{18}{\rm cm^2} }\right)
\left({r_{ex}\over 0.95 r_\oplus}\right)^{1/2}\left({M_p\over 0.81M_e}\right)^{-1/2}\left({{{c_s^2/(v_w^2 \Gamma)} +1}\over 1.00}\right){\rm g/s},
\end{array}
\label{mdotplanet2mom}
\end{equation}
where in both Eq. (\ref{mdotplanet2}) and (\ref{mdotplanet2mom}) we have
used $r_T$ as defined in Eq. (\ref{rT}) with $r_g$ computed for
$O^+$ ions  at the solar wind speed  using a Parker spiral field  \citep{Parker1958}
 estimate for the  uncompressed  wind magnetic field  $B(R)= B_\odot (R_\odot^2/ R) (\Omega_\odot/v_w)$ at Venus' distance from the sun.  This provides a maximum estimate  for $r_g$ since a  larger field and smaller thermal speed lowers $r_g$.  The result is
\begin{equation}
r_g=  9.9\times 10^8 {\rm cm}\left({\mu\over 16}\right)\left({v_w\over 4\times 10^7{\rm cm/s}}\right)\left({B\over 7\times 10^{-5} {\rm G}}\right)^{-1}.
\label{31}
\end{equation}
For $\mu=16$, the  corresponding ion loss rates are then
\begin{equation}
dn/dt \le  {{\dot M}_{out\venus} \over \mu  m_p}\simeq

  5.58 \times 10^{28}

   {\rm s}^{-1}
\label{32}\end{equation}
and
\begin{equation}
dn/dt \le  {{\dot M}_{out\venus} \over \mu  m_p}\simeq
1.44\times 10^{27}

  {\rm s}^{-1}.
\label{33}
\end{equation}
This  latter limit is an order of magnitude  larger than the highest values reported in \citep{Knudsen1992,Dubinin2011+} for ions above the escape energy.

For Mars, aside from its localized magnetic features, much of the surface has too
little magnetic or ionospheric pressure to steadily abate the incoming wind ram pressure \citep{Russell2016+}.
We again use Eq. (\ref{mdotplanet2})

but now with the Martian parameters of $M_p =0.11M_e$; $r_p\sim r_s=r_{ex}=0.53 r_\oplus$,
and $R=1.5AU$ in Eqn. (\ref{outboth}).
For  $r_T$ we  use  Eq. (\ref{rT}) but
 employing Mars' radius for  $r_p$
and   $r_g$  is now the gyro-radius for $O_2^+$ ions moving at  the solar wind speed in  the uncompressed solar wind field at Mars, namely,
$
r_g=  4.2\times 10^9 \left({\mu\over 32}\right)\left({v_w\over 4\times 10^7{\rm cm/s}}\right)\left({B\over 3.3\times 10^{-5} {\rm G}}\right)^{-1}{\rm cm}$.

The resulting  mass loss limit from  energy conservation from Eq. (\ref{outboth}) is then
${\dot M}_{out\mars}=1.3\times 10^{5}$g/s and
for $\mu=32$, the corresponding ion loss rate is then
\begin{equation}
dn/dt \le  {{\dot M}_{out\mars} \over \mu  m_p}\simeq
2.3\times 10^{29}
 {\rm s}^{-1}.
\label{34}
\end{equation}
If instead we use  momentum conservation in Eq. (\ref{outboth}), then we obtain
${\dot M}_{out\mars}=1.6\times 10^{3}$g/s and the corresponding ion loss rate  limit of
\begin{equation}
dn/dt \le  {{\dot M}_{out\mars} \over \mu  m_p}\simeq

  2.9 \times 10^{27}

  {\rm s}^{-1}.
\label{35}
\end{equation}
These can be compared with values up to
$2\times 10^{25}/{\rm s}$ at solar max reported in
\cite{Dubinin2011+}.

Comparing the results from Eqs. (\ref{27}) \& (\ref{28});  (\ref{32}) \& (\ref{33}); and
and (\ref{34}) \& (\ref{35}) we see that (i)
the  wind-induced mass loss  limit estimates from energy conservation span 2 orders of magnitude  with ${\dot M}_{out\mars} > {\dot M}_{out\venus}> {\dot M}_{out\oplus}$,  and all exceed the respective limits from momentum conservation for each of the three cases;  (ii)  the mass loss limits from momentum  conservation  satisfy the same inequality ordering but   all are within an order of magnitude of each other;   (iii)   the momentum limits are all appropriately  larger than the largest measured values.   It is a worthy pursuit to identify the basic principles that dictate how efficiently the incoming energy and momentum are redistributed among particles and on what this depends.  Momentum limits may be more pertinent than energy limits for  unmagnetized planets as the flow has more direct access to the atmosphere. In addition, we might speculate that the maximum efficiency with which momentum is converted to oxygen ions given the aforementioned comparisons of predicted versus measured values is of the order of 10\% for Earth and Venus and 1\% for Mars.  The latter is perhaps consistent with the possibility emerging from at least one global model, namely  that photodissociation may dominate Mars' present ion loss, but
that of ancient Mars  ($\sim 4$ Ga) was two orders of magnitude larger, and dominated by ion-pickup \citep{Dong2018b+}.  That said, the relative role of photodissociation
vs. ion-pickup is still an area of active study.
However,  given the current limitations on observed loss rates and incoming wind flux,
 these pursuits are left  for future study.

In short, our formalism  may help to explain aspects of the present-day loss rates of  terrestrial planets with atmospheres.  We reiterate that this is separate from the  specific question of the role of magnetic fields in sustaining or inhibiting habitability.
The  present state of Venus and Mars
reflects a longterm atmospheric evolution with  a profound loss of the principal component defining habitability--water.  Present day Venus is particularly inhabitable.
As such, the  present-day atmospheric erosion rates  do not provide  direct  measures of  depletion of a specifically habitable atmospheres but
still offer   testbeds for  basic principles of
atmospheric mass loss given different sources of external stellar forcing.
Those principles are still important to identify even if they do not comprise
a  complete set of ingredients that determine habitability. }

\section{Conclusions}

We have considered how a planetary magnetosphere influences the upper limit on stellar wind induced mass loss  by focusing on   how the magnetic field affects  incoming flow  of
mass and energy into the atmosphere. The approximate maximum outflow rates are estimated separately for the constraint of energy conservation and momentum conservation assuming that  (i) all of the incoming energy or momentum goes into  outgoing particles just at the escape speed; and (ii) that the atmospheres have initially thermal energy distributions  with most probable speeds initially less than 1/4 the escape speed. Our  formalism  can be used to obtain  upper limit estimates for a given planetary magnetic field, planet size, mass, orbital radius and stellar wind parameters.
For the parameter regimes considered, momentum conservation provides a lower upper limit than energy conservation.

The  formalism may be helpful toward a better understanding of the role and extent that magnetic fields play in protecting atmospheres of  both solar system and extrasolar planets.
In particular, we find that the competing
effects of decreased solar wind flux interacting with the atmosphere versus increased solar wind collection area predict that (i) for most of Earth's history, more total solar wind mass may have been captured with potential to interact with the atmosphere than would have been the case without a geodynamo but that (ii) the geomagnetic field still had a net protective from the solar wind  because less wind energy was input as compared to would be the case of an unmagnetized Earth.
However, when polar focusing is taken into account,  the future  polar energy flux collected by Earth's magnetosphere could exceed that which would be collected without a field.  The latter implies that the future protective effect of the geomagnetic field will depend primarily on its ability to recapture \citep{Seki2001} otherwise ablated plasma.
We also showed how the competing effects of decreased solar wind flux interacting with the atmosphere versus increased solar wind collection area
might contribute to explaining the explain present-day oxygen ion ejection rates from Earth, Mars, and Venus.

Since the retention of water, and therefore oxygen, is a  key ingredient for Earth-like habitability,  our results highlight that the influence of planetary magnetic fields on the survival of  habitable atmospheres must ultimately depend on the relative interplay  between  incoming wind flux reduction,  increase wind capture area, and outgoing atmosphere re-capture.

\section*{Acknowledgments}
 { We thank  J. Carroll-Nellenback and J. E. Owen for useful related discussions and the referee
for thoughtful and  useful comments.
  EB acknowledges  support from National Science Foundation (NSF) and
  Hubble Space Telescope (HST) grants
 NSF-AST-1109285 and HST-AR-13916.002, respectively, and from the Simons Foundation,  the Institute for Advanced Study (Princeton) and the Kavli Institute for Theoretical Physics of UCSB with support from NSF grant PHY-1125915.
 JAT acknowledges  support from grants NSF-EAR-1656348
 and NSF-EAR-1520681.}

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