Doug Christenson brings 31 years of retail and executive automotive knowledge to our company in both the Variable and Fixed operations. A native of Flint, Michigan, Doug's career began on the GM assembly line, progressed to the retail side and now includes New, Pre-Owned and Finance Director experience. As National Field Operations Manager for Sonic Automotive, he coordinated due diligence operations as part of their acquisition team.
Doug was one of the original six members inside Sonic Automotive Group given the responsibility to create Sonic University and served as an instructor for their Dealer Academy as well. Today, he is equally adept training with the Wall Street metrics of publicly held dealer groups and at the same time, bringing his knowledge to our single point dealerships who value his ability to relate directly to their long-standing family and community traditions.


Louis Eschenauer Medoc AOP comes from the region of France called Medoc, where best and the most exceptional wines are born. It has a rich red color, fading to purple, and a strong aroma of red fruits, plums and black currant. Oak taste is something, that is specific for wines of this region as well.


Reserved for exclusive use by our corporate day guests, Mill Cottage is the perfect base to enjoy your day at Kimbridge.
Situated in a beautiful position on the banks of the River Test, Mill Cottage was originally built as two cottages in 1906, where the chauffeur and gardener of the estate owner both lived. In recent years it has been combined into a single house, restored and transformed into a comfortable and relaxing fishing lodge.
The original mill at Kimbridge was still grinding corn at the turn of the 19th century. Today only the water wheel remains, which still generates electricity. The structure of the mill is captured in this 1900 photograph. The mill has gone. In its place stand a workshop, a garage and Mill Cottage. Interestingly, the white railings of the river bridges to the rear of the wagon along Kimbridge Lane still survive to this day.
The sound of the turning mill wheel and the gently sloping lawn, leading down to the waters edge, both add to the charm and tranquillity of the cottage and its surroundings.
Mill Cottage can accommodate up to 6 guests in three double bedrooms and one twin room. It has three airy bathrooms and a downstairs WC. The large traditional farmhouse style breakfast kitchen is fitted with all the latest appliances. A tackle room is provided to safely store all your rods and fishing equipment. The cottage is double-glazed and centrally heated throughout, with the added benefit of a real log-burning stove in the living room and kitchen for those chilly early autumn evenings.
The formal dining area, with large French windows leading out onto the spacious terrace, is regularly used for corporate day lunches and evening buffets. Garden furniture is laid out on the terrace for relaxing over a sundowner on those balmy summer evenings.
Mill Cottage operates a no smoking policy in all rooms.


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An avid bug hunter has discovered a vulnerability in Valve's Steam developer portal which, exploited properly, reveals every license key for every game available on the platform. Instead of selling the keys for illicit profit, he reported the flaw to Valve.
Artem Moskowsky discovered the bug in August, but Valve published the news only recently, taking enough time to patch the flaw and make sure it can never be exploited again.
Moskowsky reportedly stumbled across the bug by mistake, while taking an innocent stroll down Valve's developer site, where game sellers can manage their titles.
"This bug was discovered randomly during the exploration of the functionality of a web application. It could have been used by any attacker who had access to the portal," Moskowsky told the news site.
In one case, Moskowsky says he obtained 36,000 license keys for the relatively old (but still relevant) Portal 2 game, developed by Valve itself. The game retails for $9.99, which (theoretically) would translate into around $359,640 in lost revenue for the developer, if the keys got sold on the black market.
The researcher reported the flaw via HackerOne, the bug bounty program that connects businesses with cybersecurity researchers in an effort to find and fix bugs before unethical hackers beat them to it.
Valve awarded Moskowsky the $15,000 bounty — plus an additional $5,000 because the company felt he deserved an extra bonus for the find. The Register notes that Moskowsky previously got a $25,000 reward for finding a vulnerability in the exact same platform. Looks like ethical hacking does pay!
Impressive, but such revenue loss would have raised the alarms sooner than later. Anyway, it is nice to see that bug bounty programs just work.


Happy Mother's Day Weekend! In addition to all the kart stuff going on, it's Mother's Day. Yes, our moms let us race on Mother's Day, and they are awesome. It's also Jason's birthday on Monday, so Happy Birthday too!!
Wild Duck Racing returned to the track that started Jason's road racing career, with new karts. Almost 5 years ago to the day we first visited Gateway Motorsports Park for our first ever Championship Enduro Series road race. Back then Jason was driving an LO206 powered kart in the Junior Novice class. He was not fast compared to our competition but that was not really the point. This year, we brought the sprint kart and the new road kart. Both Briggs and Stratton Animal powered and both fast. Back then he was running laps in 1:40+. This weekend he ran 1:20 in both karts.
We arrived on Friday afternoon and set up our pit area in the garage. Gateway has one of my favorite garage areas because it comes with power and air. We get to use the same garages that the NASCAR Truck Series and Indy Series use a few weeks later. One of the highlights of Friday night was a impromptu interview of Jason by a karting blogger and our Amsoil supplier TJ Hollingsworth of MidLife Karting Crisis fame and owner of Winning Synthetics. I step away and let Jason do his own interviews without any coaching during it, but we do practice occasionally and he pays attention to the kart and what's going on with it during the race day.
Saturday started with practice, Jason decided to run the road kart in the break-in session to start get a feel for it, and then ran it with the first 4 cycle session. It ran ok for a few laps, until he pulled in complaining that the motor was burping in the corners. This problem would plague us all weekend and was not solved until the Sunday's race. The sprint kart was amazing, it was fast and just needed some slight gear changes to optimize. It was fast enough that he practiced with the 2 cycle group and had no troubles with with traffic.
Once practice was over things really fell apart. I found that the sprint frame had broken on the right side and needed to be welded. In the meantime Jason took the road kart to the 4 cycle central pit for some investigation. While there, he was grabbing tools and tearing down the motor so Regan could take a look and hopefully find the issue. This was a real first. Jason put forth a great effort working on that kart trying to get it back into racing shape, unfortunately everything checked out and we need to keep looking for the problem.
While putting the newly-welded sprint kart back together, I found that one of the rear seat struts was also cracked and needed to be replaced. With only 15 minutes before the race start. I was really thrashing on the kart to get it fixed. Tools and parts were flying in our pits along with some strong language. With just a few minutes to go, I managed to get the kart to the grid and just in time for the start, only because the start was delayed by some other issue. Race 1 and 7 in the sprint kart went very well with Jason setting his record lap times and putting on a great show with the Animal 360 karts. The road kart was not as successful. He got to start the race and pulled in after the first lap with burping issues. Back to work for the rest of the evening.
Saturday's race 1 in the sprint kart was great again. It was really dialed in and he was doing great things, working on passing and timing, and working on the draft. He is kart is as fast as the slow pack of 360s. If he continues to get the draft in the straights he should be able to really fly. We finally find the problem with the road kart: the engine was so thirsty for methanol, the fuel system was vacuum locking. However, since we did not get much practice in we did not get much tuning and it was handling poorly. During the race the rear tires broke free while exiting the corner into the big oval and it backed into a tire barrier pretty hard. Jason was checked out and was OK but his racing day was over early. The kart sustained a bit of damage. Between this and some other issues we are are forced to skip the Michigan International Speedway race since there is just too much do to get ready.
Once again thanks to Regan at 4 Cycle Central and Marty Murray for helping keep the karts on the track, and to Kat Murray and Judy and Mark Nielsen for help after the race, yummy dinner and excellent company on Friday night. Thanks to our Moms, and Grandmothers for their support and for getting us this far.


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text:
\section{Introduction}
Fast dissipation of magnetic energy is a key process feeding the luminosity of strongly magnetized objects.
A canonical example is magnetars, which produce short powerful X-ray bursts and giant flares (see \citet{2017ARA&A..55..261K} for a review).
Two possible  mechanisms of fast dissipation in magnetars have been studied: a magnetospheric turbulence cascade \citep{1998PhRvD..57.3219T, 2019ApJ...881...13L} and magnetic reconnection \citep{1996ApJ...473..322T,2003MNRAS.346..540L,2013ApJ...774...92P,2020ApJ...900L..21Y,2020arXiv201107310B}.
It is not established which mechanism dominates the observed activity.

A similar open question concerns the origin of fast dissipation in other systems, including magnetically dominated coronae and jets of accreting black holes and the Crab nebula.
Particularly challenging are the ultra-fast gamma-ray flares occasionally observed in these systems, indicating sudden dissipation events, perhaps associated with magnetohydrodynamic instabilities.
It was also proposed that fast dissipation can occur in specially prepared unstable magnetic configurations, with immediate onset of violent magnetic reconnection \citep{2016ApJ...826..115N,2018JPlPh..84b6301L}.

In this paper, we describe a different dissipation mechanism which naturally occurs in magnetically dominated systems with strong waves.
It works quickly, on the light crossing timescale, and its efficiency can reach $100\%$.
Alfv\'en waves in a magnetically dominated plasma propagate with nearly speed of light, and the wave electric field $E$ can approach the magnetic field $B$, in particular when two waves collide. When $E$ reaches $B$, the ideal magnetohydrodynamics (MHD) breaks, which causes immediate strong dissipation.
The conditions for triggering this mechanism can be seen analytically by considering two symmetric counter-propagating Alfv\'en wave packets with linear polarizations. Propagation of an isolated packet may be well described in the framework of ideal force-free electrodynamics (FFE), which neglects plasma inertia.
However, the packet collision becomes a kinetic plasma problem, because the collision is dissipative and we wish to see how the particles gain energy.

In Section~\ref{sec:theory}, we give an analytical description of the wave collision, using a simple setup of two symmetric plane waves propagating along the $x$ axis.
Then, in Section~\ref{sec:simulation}, we employ direct kinetic simulations to demonstrate the dissipation mechanism.
We first perform one-dimensional (1D) simulations, with symmetry in the $y$ and $z$ directions, and then simulate the same system in two dimensions (2D) allowing the development of instabilities along $y$ (the direction of the wave magnetic field).
Our results are summarized in Section~\ref{sec:discussion}.

\section{Analytical Description}\label{sec:theory}
\subsection{Setup} \label{setup}
The simplest setup of the wave collision problem is shown in the left panel of Figure~\ref{fig:squarewave}.
Two wave packets with a square profile are propagating in the $\pm x$ directions and collide at $x=0$.
All quantities are independent of $y$ and $z$, i.e. we deal with plane waves where the electromagnetic fields $\boldsymbol{E}$ and $\boldsymbol{B}$ are functions of $x$ and time $t$.
The constant background magnetic field $\boldsymbol{B}_0$ is uniform and directed along the $x$ axis.
The two waves are linearly polarized.
The best case for strong dissipation is where the two waves have equal electric fields $\boldsymbol{E}=(0,0,E_z)$.
The corresponding magnetic field is $\boldsymbol{B}=(B_0,B_y,0)$, with $B_y=\pm E_z$ having opposite signs for the two waves.

We will assume that the background plasma is strongly magnetically dominated, i.e. it has the magnetization parameter
\begin{equation}
    \sigma_0\equiv\frac{B_0^2}{4\pi n_0 mc^2}\gg 1,
\end{equation}
where $n_0$ is the number density of plasma particles carried by the waves, and $m$ is the particle mass.
For simplicity, we will assume that the $\pm$ charges have the same mass $m$.
This is satisfied for electron-positron plasma, which is expected in the astrophysical objects of interest.

In the limit of $\sigma_0\rightarrow\infty$, the wave propagates with the speed of light $c$, without any distortion.
As long as the two wave packets remain isolated, i.e. before the collision, their propagation does not involve excitation of electric current: the wave electric field $\boldsymbol{E}\perp\boldsymbol{B}_0$ is unable to move the magnetized $e^\pm$ particles and excite a current.
The propagation occurs as if the magnetized plasma was replaced by vacuum.
Such waves can be viewed as Alfv\'{e}n  waves with wavevectors parallel to the background field.
In this special case, the Alfv\'{e}n  wave becomes degenerate with the other FFE mode, the fast magnetosonic wave.

The dimensionless wave amplitude is defined by
\begin{equation}
    A\equiv\frac{|E_z|}{B_0}=\frac{|B_y|}{B_0}.
\end{equation}
The two wave packets will be assumed to have the same amplitude.
There is no loss of generality in this assumption, because for incoming waves with different amplitudes one can always choose a new inertial frame (boosted along the $x$ direction) where the amplitudes become equal.

The two initial packets have the Poynting fluxes
\begin{equation}
    \boldsymbol{S}=c\,\frac{\boldsymbol{E}\times\boldsymbol{B}}{4\pi}=\pm c\, \frac{E^2}{4\pi}\,\boldsymbol{e}_x-c\,\frac{EB_0}{4\pi}\,\boldsymbol{e}_y,
\end{equation}
where $(\boldsymbol{e}_x,\boldsymbol{e}_y,\boldsymbol{e}_z)$ are the unit vectors of the Cartesian coordinate system.
We will denote the magnitude of the initial Poynting flux toward the collision center $x=0$ by $S_0=|S_x|$,
\begin{equation}
  S_0=\frac{c}{4\pi}\,A^2 B_0^2.
\end{equation}
The total (free) wave energy per unit area is defined by
\begin{equation}
    U = \int \frac{E^2+B^2-B_0^2}{8\pi}\;\mathrm{d} x.
\end{equation}
It excludes the contribution of the constant background magnetic field.

It is convenient to define two characteristic frequencies of the problem,
\begin{equation}
    \omega_p\equiv \sqrt{\frac{4\pi e^2 n_0}{m}}, \qquad \omega_B\equiv \frac{eB_0}{mc}=\sqrt{\sigma_0}\,\omega_p.
\end{equation}
We will assume that the length of the wave packet $\lambda$ is much larger than the characteristic plasma scale $c/\omega_p$.
As will be shown below, $c/\omega_p$ sets the characteristic width $\Delta$ of the dissipation layer (current sheet) established during the wave collision.

\subsection{Wave Dynamics}
The dynamics of electromagnetic field is governed by the Maxwell's equations,
\begin{eqnarray}
\frac{\partial \boldsymbol{B}}{\partial t} &=& -c\nabla\times\boldsymbol{E}, \label{eqn:induction}\\
\frac{\partial \boldsymbol{E}}{\partial t} &=& c\nabla\times\boldsymbol{B} -4\pi \boldsymbol{j}.\label{eqn:ampere}
\end{eqnarray}
The vacuum-like propagation occurs as long as $\boldsymbol{j}=0$.

\begin{figure*}
\includegraphics[width=0.98\textwidth]{squarewave.pdf}
\caption{
Collision of two symmetric plane  waves with equal amplitudes $A$ ($A>1$ is assumed in the figure).
Left: the fields in the two wave packets before the collision.
Middle: the fields during the collision (blue).
Two reflected waves with $E_z=B_0$ become superimposed on the incoming waves in a growing region (shaded in grey).
The jump of $B_y$ at the center has changed from $\pm AB_0$ to $\pm(2A-1)B_0$.
For comparison, the dashed orange line shows how the two packets would propagate through each other in vacuum (this would apply if $A<1/2$).
Right: the two packets after the collision (blue).
The reflection with amplitude $A-1$ is now complete and the reflected packets are moving away from the center.
The final state is different from free propagation of the packets through each other (orange).
}
\label{fig:squarewave}
\end{figure*}

Consider first what would happen if the current density $\boldsymbol{j}$ remained everywhere zero when the two wave packets approach and overlap.
Then, the waves would continue their linear evolution and keep propagating with speed $c$.
The electromagnetic field would be described simply by the superposition of the two waves, as shown by the orange dashed lines in Figure~\ref{fig:squarewave}.
Where the two waves overlap, their opposite magnetic fields cancel, and their equal electric fields add up, so
\begin{equation}
    B_y=0,\qquad |E_z|=2AB_0.
\end{equation}
The overlapping region expands with speed $2c$ until the two symmetric packets totally overlap.
Then, the overlapping region begins to shrink and eventually vanishes, after the two waves pass through each other and exit the collision with no change from their original form.
In the ovelapping region we find
\begin{equation}
    E^2-B^2 = B_0^2(4A^2-1) \qquad
    \left(\textrm{for} \; A<\frac{1}{2}\right).
\end{equation}
This relation holds as long as $E<B$, which requires $A<1/2$.

For amplitudes $A>1/2$, the magnetic dominance is broken.
Then, the collision cannot occur with $\boldsymbol{j}=0$.
Plasma particles exposed to $E>B$ are no longer magnetized, and $e^\pm$ are accelerated by $\boldsymbol{E}$ along $\pm z$, creating an electric current $\boldsymbol{j}=(0,0,j_z)$.
The current excitation will buffer the growth of $\boldsymbol{E}$ in the collision region.
It tends to screen $\boldsymbol{E}$ similar to the well known screening of low frequency electromagnetic waves in unmagnetized plasma.
The screening occurs on the short timescale $\sim\omega_p^{-1}\ll \lambda/c$, i.e. immediately after reaching $E>B$.
It prevents any significant growth of $E>B$, so that $E$ in the collision region is bound by
\begin{equation}
  E_{\rm screen}=B \qquad \left(\textrm{for} \; A>\frac{1}{2}\right).
\end{equation}
Note that $B_y=0$ at $x=0$ at all times, by symmetry.
Therefore, $B=B_0$ at the collision center.
Thus, the presence of plasma imposes a simple boundary condition for the wave collision problem,
\begin{equation}
    |E_z|=B_0,\qquad B_y=0 \qquad (x=0).
\end{equation}

This condition allows one to quickly find the evolution of the electromagnetic field during the packet collision.
The plane $x=0$ reflects the incoming waves with amplitude $\boldsymbol{E}_r$ such that the total $E=B_0$.
It turns out sufficient for the system to create a thin current sheet at $x=0$ (where it is easiest to break magnetic dominance), and outside the current sheet the reflected waves propagate in the linear, vacuum regime.
The validity of magnetic dominance $B>E$ (and hence $j=0$) can be verified after the wave reflection solution is obtained from the boundary value problem.
This solution will also be verified below by the direct kinetic simulation of the plasma behavior in the colliding waves.

The problem is symmetric about the plane $x=0$, so two symmetric reflected waves will be launched, with equal amplitudes $A_r=|\boldsymbol{E}_r|/B_0$.
They propagate away from $x=0$ on top of the two original incoming waves with amplitude $A$.
The reflected wave has electric field $\boldsymbol{E}_r=(0,0,E_{z,r})$ such that the total electric field satisfies $E=B_0$. This gives
\begin{equation}
  A_r=|A-1|.
\end{equation}
$E_{z,r}$ has the same sign as the incoming wave if $A<1$, and changes sign if $A>1$.
The magnetic field of the reflected wave $\boldsymbol{B}_r$ satisfies $|B_{y,r}|=|E_{z,r}|$, and its sign is such that the wave propagates away from $x=0$: $\boldsymbol{E}_r\times\boldsymbol{B}_r$ is along $\boldsymbol{e}_x$ at $x>0$ and along $-\boldsymbol{e}_x$ at $x<0$.

Note that the reflected wave vanishes when $A=1$; in this special case the incoming waves are completely absorbed at the collision centre, yielding the maximum dissipation efficiency.
This will be confirmed below by the 1D and 2D kinetic simulations. The limit of $A\gg 1$ gives $A_r/A\approx 1$, suggesting an ``elastic'' collision -- the two packets bounce from each other with negligible absorption.
This elastic behavior holds only in the 1D model.
We will show in Section~\ref{sec:sim2d} that the 1D description fails when $A\gg 1$; then a different dissipation mode is activated by the tearing instability of the current sheet.

The superposition of the incoming and reflected waves determines the electromagnetic field during the collision of packets with $A>1/2$.
It is shown in Figure~\ref{fig:squarewave} for the case of $A>1$.
After the collision is over, only the reflected waves are left.
Note that $A>1$ gives the fields in the final state with signs opposite to the vacuum solution that was found for $A<1/2$.
When the initial amplitude satisfies $1/2<A<1$, the final fields have the same signs as the original waves, as if the packets have propagated through each other and came out with a reduced amplitude $|A-1|=1-A$.
When $A\rightarrow 1/2$ the solution obtained using the reflected waves becomes identical to free propagation of the initial waves through each other.

During the collision of packets with $A>1/2$, $B_y$ in the interaction region (the grey stripe in Figure~1) does not cancel to zero.
The superposition of the incoming and reflected waves gives
\begin{equation}
\label{eq:By}
    |B_y|=(2A-1)B_0,
\end{equation}
and $B_y$ has the opposite signs at $x>0$ and $x<0$.
Equation~(\ref{eq:By}) implies that $B>E$ everywhere except the narrow layer at $x=0$ where $B_y$ changes sign.
The excitation of electric current becomes possible in this layer because $B_y=0$ (at $x=0$) allows $E$ to approach $B$.
The surface electric current sustaining the jump of
$B_y$ at $x=0$ is given by
\begin{equation}
\label{eq:I}
I=\frac{c|B_y|}{2\pi} = \frac{(2A-1)cB_0}{2\pi}.
\end{equation}
Outside the narrow central layer the waves propagate as in vacuum ($j=0$), giving the simple linear superposition of the incoming and reflected waves.

The fact that the reflected wave amplitude is reduced from $A$ to $|A-1|$ implies that the following fraction $f$ of the incoming Poynting flux $S_0$ is absorbed at $x\approx 0$,
\begin{equation}\label{eqn:frac_dis}
    f=\frac{A^2-(A-1)^2}{A^2}=\frac{2A-1}{A^2}.
\end{equation}
The power absorbed per unit area, from each side $\pm x$, is $fS_0=fA^2B_0^2c/4\pi$.
The electromagnetic power absorbed from both sides equals the power dissipated in the current sheet,
\begin{equation}
\label{eq:power}
    2fS_0=EI=B_0I.
\end{equation}
This self-consistency check completes the basic description of the electromagnetic field during the wave collision.

\subsection{Particle Dynamics}
\subsubsection{Particle Motion outside the Current Sheet}
Let us first consider particle motion in the isolated wave, before the collision begins.
The wave packet has uniform orthogonal fields $\boldsymbol{E}$ and $\boldsymbol{B}$, and the particle motion in this situation is well known (Appendix~\ref{sec:app_motion1}).
The electromagnetic field of the packet satisfies
\begin{equation}
\frac{E}{B}=\frac{|E_z|}{(B_0^2+B_y^2)^{1/2}}=\frac{A}{\sqrt{1+A^2}}<1.
\end{equation}
Therefore, the particle motion on timescales $\gg\omega_{B}^{-1}$ is a drift in the direction of the Poynting flux with velocity   $\boldsymbol{v}_{\rm d}=c\,\boldsymbol{E}\times\boldsymbol{B}/B^2$.
Note that $\boldsymbol{E}\times\boldsymbol{B}=(-E_zB_y,E_zB_0,0)$ has the non-zero $x$ and $y$ components.
The Poynting flux and the particle drift in the $y$ direction are not causing any interesting transport, because the system is symmetric under translation along $y$.
The drift speeds along $x$ in the isolated packets before the collision are
\begin{equation}
    v_{{\rm d},x}^0 = \frac{E_zB_y}{B^2}c=\pm\frac{A^2}{A^2+1}\,c.
\end{equation}
The particles are drifting in the direction of the wave packet propagation toward the future collision center.
The Lorentz factor of the particles is
\begin{equation}
    \gamma_{\rm d}^0 = \frac{1}{\sqrt{1-(v_{\rm d}^0/c)^2}}
    = \sqrt{A^2+1}.
\end{equation}

We consider here waves in a magnetically dominated plasma, so that the group Lorentz factor of the wave, $\gamma_{\rm gr}\approx \sigma_0^{1/2}$ can be taken as infinity in the first approximation, i.e. the wave packet propagates with speed $c$.
The particle drifts relative to the packet with speed $|v_{{\rm d},x}^0|-c=-c/(A^2+1)$, and it takes time
\begin{equation}
  t_{\rm cross}=\frac{\lambda}{c-|v_{{\rm d},x}^0|}=(A^2+1)\,\frac{\lambda}{c}
\end{equation}
for the particle to cross the packet of length $\lambda$ and exit behind it.

The particle number density inside the packet, $n_0$, obeys the continuity equation.
For instance, consider the packet propagating in the $+x$ direction. Using the coordinate $\xi=x-ct$, the continuity equation for the plasma with density $n(\xi,t)$ and speed $v_x(\xi,t)$ reads
\begin{equation}
    \frac{\partial n}{\partial t}+\frac{\partial}{\partial \xi}\left[n(v_x-c)\right]=0.
\end{equation}
In a steady state ($\partial/\partial t=0$), this yields
\begin{equation}
\label{eq:n}
    n_0 = \frac{n_b}{1-v_{{\rm d},x}^0/c}=(A^2+1)n_b,
\end{equation}
where $n_b$ is the unperturbed plasma density ahead (and behind) the wave packet, where  $v_x=0$.

After the collision begins, the particles swept by the packets with $A>1/2$ will encounter the reflected wave.
Then they become exposed to the electromagnetic field  that satisfies $|E_z|=B_0$ and $|B_y|=(2A-1)B_0$, and continue to drift toward the center with a reduced speed
\begin{equation}
\label{eq:vdx}
v_{{\rm d},x}=\pm\frac{|E_z B_y|}{B_0^2+B_y^2}c
=\frac{(2A-1)}{4A^2-4A+2}c.
\end{equation}
The density of the particles coming toward $x=0$ is then changed to
\begin{equation}
  n=\frac{c+|v_{{\rm d},x}^0|}{c+|v_{{\rm d},x}|}\,n_0.
\end{equation}
Note that the jump of the drift speed from $v_{{\rm d},x}^0$ to $v_{{\rm d},x}$ across the front of the reflected wave can be thought of as a shock wave.
The shock is mildly relativistic and the energy it can dissipate per particle is small compared to the power released in the current sheet at the collision center (Equation~\ref{eq:power}), which scales with $\sigma_0\gg 1$.

\subsubsection{Particle Motion inside the Current Sheet}
We now examine in more detail the plasma behavior in the dissipative collision of waves with $A>1/2$.
The particle number flux from each side toward $x=0$ is
\begin{equation}
    F=n\,|v_{{\rm d},x}|=\frac{(2A^2+1)(2A-1)}{(A^2+1)(4A^2-2A+1)}\,cn_0,

\end{equation}
and the Poynting flux absorbed at the collision center is
\begin{equation}
    S_{\rm abs} = fS_0= \frac{c}{4\pi} (2A-1)B_0^2.
\end{equation}
This implies that on average the particles passing through the dissipation region gain the Lorenz factor
\begin{equation}
\label{eq:gam_av}
    \bar{\gamma}\approx\frac{S_{\rm abs}}{Fmc^2}\approx \frac{(4A^2-2A+1)(A^2+1)}{2A^2+1}\,\sigma_0,
\end{equation}
where we have neglected the particle Lorentz factor $\gamma\sim 1$ before the collision.

The conversion of Poynting flux $S_{\rm abs}$ to plasma energy occurs in the thin layer $|x|<\Delta$ occupied by the current sheet, where $B_y$ changes from $bB_0$ to $-bB_0$ ($b= 2A-1$, see Equation~(\ref{eq:By})).
The motion of particles entering the dissipation layer is described in Appendix~\ref{sec:app_motion}.
The profile of the magnetic jump $B_y(x)$ and its half-width $\Delta$ self-organize so that the particle motion in the layer self-consistently sustains $j_z=(c/4\pi)dB_y/dx$.
As discussed in Appendix~\ref{sec:app_motion}, this is achieved when
\begin{equation}
\label{eq:Delta0}
    \frac{b\omega_B\Delta}{\bar{\gamma}^{1/2} c}\sim 1.
\end{equation}
Then, using Equation~(\ref{eq:gam_av}), we find
\begin{equation}
\label{eq:Delta}
    \Delta\sim \frac{c}{\omega_p}.
\end{equation}

The time spent by the particles in the dissipation layer is (see Equation~(\ref{eq:delta_t1}))
\begin{equation}
\label{eq:delta_t}
    \delta t\sim \frac{ \bar{\gamma}^{3/2}}{\omega_B},
\end{equation}
and the column plasma density in the layer may be estimated as
\begin{equation}
    N\sim 2F\,\delta t\sim 2\,\frac{S_{\rm abs} \gamma^{1/2}}{mc^2\omega_B} \sim \frac{(2A-1)B_0}{2\pi e}\,\bar{\gamma}^{1/2}.
\end{equation}
The net electric current in the layer is $I\sim eN|\bar{v}_z|$, where $\bar{v}_z\sim - c/\bar{\gamma}^{1/2}$ (Equation~\ref{eq:vz_av}).
This gives $I$ consistent with Equation~(\ref{eq:I}), as expected.

The steady-state density of accelerated particles inside the dissipation layer is
\begin{equation}
\label{eq:nacc}
    n_{\rm acc}\sim \frac{N}{\Delta}\sim \bar{\gamma}\, n_0.
\end{equation}
The accelerated particles continually spread from the layer in the $\pm x$ directions with velocity $v_x\sim\pm c/b\bar{\gamma}$ (Equation~\ref{eq:vx}), and by the end of the packet collision occupy the region $|x|\lesssim \lambda/\bar{\gamma}\ll \lambda$.
This dense slab of accelerated particles contains the energy dissipated by the wave collision.
\footnote{After the collision ends, the current $I$ decays and emits additional waves, returning some energy of the accelerated particles to the electromagnetic field.
When $\lambda\gg \bar{\gamma}\Delta$, this residual emission phase is short compared to the main, quasi-steady phase of the packet collision, and it weakly affects the net dissipation efficiency.}
We are particularly interested in  macroscopic wave packets with
\begin{equation}
    \lambda\gg \bar{\gamma}\,\Delta.
\end{equation}
Then the collision duration$\lambda/c\gg \delta t$, so dissipation occurs quasi-steadily, and the slab occupied by the energized particles is much thicker than the dissipation layer $\Delta$.

\section{Kinetic Simulations} \label{sec:simulation}
We perform kinetic simulations of wave collision with the particle-in-cell code TRISTAN-MP \citep{2005AIPC..801..345S}.
The code calculates the evolution of $\boldsymbol{E}$ and $\boldsymbol{B}$ fields from Maxwell equations discretized on a Cartesian grid.
The electric current in each grid cell is found by following the motions of individual particles.

The setup of initial conditions is similar for the 1D and 2D simulations.
It represents two counter-propagating plane waves, as described in Section~\ref{setup} and illustrated in the left panel of Figure~\ref{fig:squarewave}.
Our fiducial model has the magnetization parameter $\sigma_0=20$.
The box is initially filled with cold neutral $e^\pm$ plasma moving with the drift velocity $c\,\boldsymbol{E}\times\boldsymbol{B}/B^2$.
The plasma has a uniform density $n_0=n_++n_-$, which defines the reference plasma frequency $\omega_p=(4\pi e^2 n_0/m)^{1/2}$.
The initial density $n_0$ is represented by $64$ particles per cell.

In all 1D simulations (and most of 2D simulations) the wave packets have the size of $\lambda=3072\,c/\omega_p$. The square profile of each packet is smoothed at the edges by adding exponential wings of width $ 50\,c/\omega_p$.
The computational box has $51200$ cells in the $x$ direction, with $8$ cells per skin depth $c/\omega_p$.
The box size is chosen slightly larger than $2\lambda$, so that it accommodates the two packets.
The choice of boundary conditions at the $x$ boundaries of the box is not important, because the packet collision ends before the waves emerging from the collision reach the boundaries.
The plasma near the boundaries remains at rest throughout the simulation, and we use the simple periodic boundary conditions.

The initial separation between the packets (not including the wings) is $128\,c/\omega_p$.
The main collision phase begins when the flat parts of the two packets approach $x=0$, which occurs after time $\sim 64\omega_p^{-1}$. We choose $t_0=-64\,\omega_p^{-1}=-0.02\,\lambda/c$ at the start of the simulation, so that $t=0$ approximately corresponds to the beginning of the strong packet collision.

\subsection{1D Simulations} \label{sec:sim}
In the 1D simulations, the electromagnetic field is not allowed to spontaneously develop any variations in the $y$ or $z$ directions during the wave collision.
In addition, the symmetry of $e^\pm$ motions in the symmetric setup of the wave collision implies $E_x=B_z=0$ throughout the 1D evolution.
Numerical noise caused by the finite number of particles can violate this condition, and then fluctuations of $E_x$ and $B_z$ can grow over time.
These fluctuations should disappear in the limit of $n_0 c/\omega_p\rightarrow \infty$, which is adequate for most astrophysical objects, however this fluctuation-free limit is expensive to simulate.
Instead, we simply impose $E_x=B_z=0$ in the 1D simulations.\footnote{We also performed simulations where numerical fluctuations of $E_x$ and $B_z$ are allowed to grow.
These noisier numerical models demonstrate similar dissipation and particle acceleration during the wave collision.
We verified that the spontaneous growth of $E_x$ and $B_z$ is reduced with increasing number of particles per cell.
}

\begin{figure*}[t]
\includegraphics[width=\textwidth]{snapshots.pdf}
\caption{Three snapshots of the 1D simulation with $\sigma_0=20$ and the initial amplitudes of the colliding packets $A=1.5$.
The wave evolution agrees with the expected picture
shown in Figure~\ref{fig:squarewave}.}
\label{fig:snapshots}
\end{figure*}

\begin{figure}[t]
\includegraphics[width=0.45\textwidth]{current.pdf}
\caption{Zoom-in of the region around the collision center $x=0$ from the simulation shown in Figure~\ref{fig:snapshots} ($\sigma_0=20$ and $A=1.5$).
Top: current density $j_z(x)$ in units of $j_0\equiv AB_0\omega_p/4\pi$ and magnetic field $B_y(x)$ in units of $B_0$.
Bottom: plasma density $n$ normalized to the pre-collision density $n_0$.
Curves with different colors correspond to different times $t$ indicated in the inset in the top panel.
The curves of $j_z(x)$ (and $B_y(x)$) are nearly identical at different times, demonstrating that the current sheet is in a steady state.
The evolving curves of $n(x)$ demonstrate the slow, quasi-steady spreading of the dense layer of particles that have passed through and escaped the current sheet.
}
\label{fig:current}
\end{figure}

\begin{figure}[t]
\includegraphics[width=0.45\textwidth]{mushroom.pdf}
\caption{Bottom: snapshot of the particle distribution in phase space (energy and position) at $t=0.8\lambda/c$, from the simulation with $\sigma_0=20$ and $A=1.5$.
Color shows $d(n/n_0)/d\ln\gamma$ as indicated by the color bar.
Top: A similar plot for $d(j_z/j_0)/d\ln\gamma$.
The black curve in each panel shows $j_z(x)$ (in arbitrary units), indicating the current sheet location.
}
\label{fig:mushroom}
\end{figure}

Figures~\ref{fig:snapshots}-\ref{fig:phase} show the results of a sample simulation with $\sigma_0=20$ and $A=1.5$.
The results are consistent with the analytical description in Section~\ref{sec:theory}.
We observe that the collision launches two symmetric reflected waves with amplitudes $A-1=0.5$ (Figure~\ref{fig:snapshots}) and a quasi-steady current sheet is sustained at $x=0$ with width $\Delta\sim c/\omega_p$ (Figure~\ref{fig:current}).

\begin{figure}[t]
\includegraphics[width=0.45\textwidth]{phase.pdf}
\caption{
Top: snapshot of a particle population in phase space (energy and position) at $t=0.8\lambda/c$, from the simulation with $\sigma_0=20$ and $A=1.5$.
The particles (positrons) were drawn according to their initial position $x_0$ at the beginning of the simulation; the particles were sampled uniformly in $|x_0|$ and traced throughout the simulation.
The color code for $|x_0|$ is shown next to the figure; red particles are initially close to the center, and blue particles are initially far from the center,
Bottom: the same set of particles is shown on the $x$-$v_z$ plane, at the same time $t=0.8\lambda/c$. The concentration of positrons with $v_z<0$ near $x=0$ sustains the electric current sheet.
The black curve in each panel shows $j_z(x)$ (in arbitrary units), indicating the current sheet location.
}
\label{fig:phase}
\end{figure}

To examine the plasma dynamics during the collision process, we traced a large sample of individual particles, starting from their initial positions $x_0$ at the beginning of the simulation and till the end of the packet interaction.
Particles in the wave packet initially drift toward $x=0$ with speed $|v_{{\rm d},x}^0|=c\,A^2/(A^2+1)\approx 0.7c$.
They also have the $y$-component of the drift motion $v_{{\rm d},y}^0=cE_zB_x/B^2=v_{{\rm d},x}^0/A\approx 0.46c$, and their initial Lorentz factor is $\gamma_{\rm d}^0=(A^2+1)^{1/2}\approx 1.8$.
When the particle encounters the reflected wave, its drift speed drops to $v_{{\rm d},x}\approx 0.4$ according to Equation~(\ref{eq:vdx}).

When the drifting particle arrives to the collision center and enters the current sheet, it gains a high Lorentz factor over the timescale $\delta t$ given in Equation~(\ref{eq:delta_t}), and then exits the current sheet.
We observe that the particles exit with Lorentz factors $\sim 80$, in agreement with the analytical result $\bar{\gamma}\approx 82$ from Equation~(\ref{eq:gam_av}).

After exiting the current sheet, the accelerated particles continue to gyrate about the magnetic field lines and also slowly slide along $\boldsymbol{B}$ away from $x=0$.
We observe that the accelerated particles form a slowly spreading cloud with density $n_{\rm acc}\sim 60 n_0$ (Figure~\ref{fig:current}), close to the analytic estimate $n_{\rm acc}\sim\bar{\gamma}n_0$ (Equation~\ref{eq:nacc}).
The acceleration inside the current sheet followed by spreading with $\gamma\approx const$ outside the sheet creates the characteristic mushroom structure in the phase space, see Figures~\ref{fig:mushroom} and \ref{fig:phase}.

Particle acceleration increases their Larmor radii, which breaks the adiabatic ($\boldsymbol{E}\times\boldsymbol{B}$ drift) description of the particle motion inside the current sheet.
As a result, the particles become capable of sustaining current $j_z$ along $\boldsymbol{E}$ (as one can see in Figure~\ref{fig:mushroom}, the electric current is dominated by the energetic particles).
This allows $j_z(x)$ to organize so that it self-consistently sustains the jump of $B_y(x)$ across the current sheet.

The process of particle acceleration in the current sheet occurs in agreement with the description in Appendix~\ref{sec:app_motion}, which uses effective potential $V$ in the boosted frame $K'$.
When viewed in the lab frame, the particle acceleration may be described similarly to \citet{1965JGR....70.4219S}.
The electrons and positrons are pushed by $E_z$ in the opposite $\pm z$ directions while the $x$-component of the Lorentz force $\pm e v_zB_y/c$ acts to confine the particles near $x=0$ between the opposite $B_y$.
The Lorentz force also causes gyration in the $zy$ plane, as $\boldsymbol{v}$ rotates about $\boldsymbol{B}_0$.
This rotation occurs on the timescale $\delta t$, converting $v_z$ to $v_y$.
Once this rotation changes the sign of $v_z$, the $x$-component of the Lorentz force no longer confines the particles and they escape with the acquired energy.

\begin{figure}
\includegraphics[width=0.45\textwidth]{fraction.pdf}
\caption{Dissipated fraction of the wave energy, measured in the 1D and 2D simulations, as a function of the wave amplitude $A$ (the magnetization parameter $\sigma_0=20$ in all the simulations).
The 1D simulations (blue crosses) reproduce the analytical result $f=(2A-1)/A^2$ obtained in the limit of $\sigma_0\gg 1$ (dashed curve).
The 2D results (red circles) deviate from the 1D results at $A\gtrsim 2$, because the current sheet at the collision center becomes tearing unstable.
}
\label{fig:energy}
\end{figure}

The dissipated fraction of the packet energy observed in the fiducial simulation with $A=3/2$ agrees with $f=8/9$ predicted by Equation~(\ref{eqn:frac_dis}).
We have also performed eight other simulations with different packet amplitudes $A$.
The results reproduced the predicted dependence $f(A)=(2A-1)/A^2$, as shown in Figure~\ref{fig:energy}.

\subsection{2D Simulations}\label{sec:sim2d}

We have run a set of 2D models with $\sigma_0=20$ and various values of $A$, from $A=0.6$ to $A=32$.
The 2D computational box is in the $xy$ plane, with the retained translational symmetry along $z$.
In most simulations, the number of cells in the $x$ direction is $N_x=51200$, the same as in the 1D model, and we use $N_y=640$ cells in the $y$ direction, with periodic boundary conditions.
We have also performed simulations with $N_x=25600$ and $N_y=2560$. The large $N_y$ becomes important if the current sheet at the collision interface develops a tearing instability, which occurs at large $A$.
We used $N_x\times N_y=25600\times 2560$ for models with $A\geq 8$, keeping the same condition of 8 cells per skin depth $c/\omega_p$.
In these models, the reduced box size in the $x$ direction requires the reduction of the packet length by a factor of 2, from $\lambda=3072\,c/\omega_p$ to $\lambda=1536\,c/\omega_p$.

The 2D models with $A<2$ show almost exactly the same evolution as the corresponding 1D models.
This may be expected, as the cross-layer magnetic field $B_x=B_0$ tends to stabilize the current sheet against the tearing instability \citep{1976JETP...43.1113G}.
We observed that the colliding wave packets are partially reflected and partially absorbed by the current sheet, exactly as in the 1D model, with the same dependence of the absorbed fraction $f$ on the wave amplitude $A$ (Figure~\ref{fig:energy}).

The stabilization effect of $B_0$ disappears at sufficiently small $B_0$ or, equivalently, at sufficiently large $A$.
We observed that in the models with $A\geq 2$, the plane symmetry of the current sheet becomes broken by the tearing instability, initiating the process of magnetic reconnection.
The development of tearing instability in the model with $A=2$ is shown in Figure~\ref{fig:current2d}.
Tearing triggers magnetic reconnection that converts $B_y$ into $B_x$ and produces closed magnetic islands  (``plasmoids'') in the $xy$ plane.
The plasmoids begin to move along the current sheet and merge.
This process is activated at $A\sim 2$ and fully develops at $A>2$, as demonstrated in Figure~\ref{fig:current2dcomp} by comparing the current sheet in the models with $A=1$, 2, and 4 at the same time $t=0.1\lambda/c$.
One can see that plasmoid merging has already produced a monster plasmoid in the $A=4$ simulation.
The merging process is slower in the model with $A=2$, and there is no plasmoid formation at $A=1$.

\begin{figure}[t]
\includegraphics[width=0.45\textwidth]{current2d.pdf}
\caption{Snapshots of current density $j_z(x,y)$ in the 2D simulation with $A=2$ and $\sigma_0=20$.
The figure shows the region near the collision centre $x=0$ where the current sheet forms.
The snapshots were taken at times $t$ indicated at the top of each panel.
One can see the development of tearing instability of the current sheet.}
\label{fig:current2d}
\end{figure}

\begin{figure}[t]
\includegraphics[width=0.45\textwidth]{current2dcomp.pdf}
\caption{Snapshots of current density $j_z(x,y)$ taken at $t=0.1\lambda/c$ in three 2D simulations with $\sigma_0=20$, which have different amplitudes of the wave packets $A=1$, 2, 4 (as indicated at the top of each panel).
Tearing instability and magnetic reconnection did not occur in the simulation with $A=1$.
At larger $A$, magnetic reconnection generated multiple plasmoids, which merged into bigger plasmoids over time, in particular in the simulation with $A=4$. }
\label{fig:current2dcomp}
\end{figure}

\begin{figure*}[t]
\includegraphics[width=\textwidth]{snapshots2d.pdf}
\caption{Three snapshots of the wave fields $B_y(x)$ and $E_z(x)$ in the 1D (blue) and 2D (orange) simulations with $A=2$ and $\sigma_0=20$.
In the 2D model, $B_y(x)$ and $E_z(x)$ were obtained by averaging along the $y$ direction.
The $x$ profiles found in the 1D and 2D models are nearly identical despite the fact that $A=2$ is sufficiently large to allow tearing of the current sheet in the 2D simulation.
}
\label{fig:snapshots2d}
\end{figure*}

In the models with $A=2, 4, 8$, the onset of magnetic reconnection has a modest effect on the wave reflection by the current sheet.
As a result, the dissipation fraction $f$ in these models does not strongly deviate from the prediction of the 1D model (Figure~\ref{fig:energy}).
Figure~\ref{fig:snapshots2d} compares the $x$ profiles of the electromagnetic fields in the 1D and 2D simulations with $A=2$ (in the 2D model, the $x$ profile was obtained by averaging the field values along the $y$ direction).
One can see that the profiles are nearly the same in the 1D and 2D simulations despite the fact that the current sheet experiences the tearing instability and breaks up into magnetic plasmoids (Figure~\ref{fig:current2dcomp}).

At yet larger wave amplitudes, $A=16$ and $32$, the 1D and 2D results strongly differ.
The 1D model predicts a small dissipation efficiency $f\approx 2/A$ at $A\gg 1$.
The 2D simulations demonstrate that magnetic reconnection due to tearing instability becomes the dominant form of dissipation, releasing $\sim 0.2$ of the wave energy.
For instance, in the 2D model with $A=32$, the dissipated fraction $f$ exceeds the prediction of the 1D model by a factor of $\sim 4$.

The value of the dissipated energy fraction in the $A\gg1$ limit can be understood as follows.
Near the reconnection layer, the magnetic field amplitude is $|B_y|\approx 2 A B_0$.
For a reconnection rate $\eta\sim 0.1$, the Poynting flux converging into the layer from each side is $S_{\rm rec}\simeq \eta c (2 A B_0)^2/4 \pi$.
Recent studies of relativistic reconnection show that roughly half of the electromagnetic energy advected into the layer converts to plasma energy \citep[e.g.,][]{sironi_15}, so the dissipated energy flux is $\sim S_{\rm rec}/2$.
This implies that the colliding waves are dissipated with efficiency
\begin{equation}
   f\sim \frac{S_{\rm rec}}{2S_0}=2\eta\sim 0.2 \qquad (A\gg 1).
\end{equation}
The reconnection process will continue as long as the incoming and reflected waves overlap near the layer, i.e., for a time of $\lambda/c$.

\section{Discussion}\label{sec:discussion}
Alfv\'en waves in a strongly magnetized plasma ($\sigma_0\gg 1$) have a special feature: the wave propagates with nearly speed of light $c$, which implies nearly equal electric and magnetic fields in the wave, $\delta E=\delta B$.
For strong waves, $A=\delta B/B_0\sim 1$, this opens the possibility for $E=\delta E$ to exceed the magnetic field $B=\sqrt{(\delta B)^2+B_0^2}$, triggering fast dissipation.
This effect is most prominent in collisions of linearly polarized Alfv\'en waves with anti-aligned $\delta \boldsymbol{B}$ and aligned $\delta\boldsymbol{E}$.
We have investigated the collision of two symmetric plane waves propagating with wave vectors $\pm \boldsymbol{k}\parallel \boldsymbol{B}_0$ in a uniform background field $\boldsymbol{B}_0$.
In this case, the problem becomes essentially one-dimensional, i.e. all quantities depend on the $x$ coordinate that runs along $\boldsymbol{B}_0$.
We have described the collision analytically and performed kinetic simulations, both 1D and 2D, allowing spontaneous breaking of the plane symmetry.
Our fiducial numerical model has $\sigma_0=20$ and $A=1.5$, and we also calculated a broad range of models with $\sigma_0\gg 1$ and $A\leq 32$.
Our results are as follows.

\begin{enumerate}
\item
Dissipation is triggered when the colliding waves have the amplitudes $A>1/2$. Waves with $A<1/2$ pass through each other without dissipation.
\item
The collision with $A>1/2$ generates a thin current sheet at the collision center $x=0$ which separates the opposite magnetic fields of the colliding waves.
The sheet serves as a wall that partially reflects and partially absorbs the incoming waves.
It self-organizes to sustain $E=B_0$, so that $E=B$ at $x=0$.
This condition determines the reflected wave amplitude $A_r=A-1$ and the absorbed energy fraction $f=(2A-1)/A^2$.
When $A=1$ there is no reflection and $100\%$ of the wave energy is dissipated, i.e. the two waves annihilate each other at the collision center.
\item
The dissipation generates particles with Lorentz factors $\bar{\gamma}\sim A^2\sigma_0$ (Equation~\ref{eq:gam_av}).
The energy conversion process is quasi-steady when the length of the colliding wave packets $\lambda\gg \bar{\gamma}\, \Delta$ where $\Delta$ is the thickness of the current sheet.
\item
The current sheet thickness is self-regulated to $\Delta \sim c/\omega_p$, where $\omega_p^2=4\pi e^2 n_0/m_e$ is defined for the plasma in the wave packet before the collision.
The colliding waves feed particles into the current sheet with a mildly relativistic drift speed.
The particles enter and then exit the sheet, gaining the Lorentz factor $\bar{\gamma}$  on the timescale $\delta t\sim \bar{\gamma}^{3/2}/\omega_B$, where $\omega_B=eB_0/mc$.
The energized particles gyrate about $\boldsymbol{B}$ and spread from the sheet (upstream into the incoming wave packet) along $\boldsymbol{B}$ with a small $v_\parallel\sim \pm c/\bar{\gamma}$.
The spreading cloud of accelerated particles has density $n_{\rm acc}\sim \bar{\gamma} n_0$, much higher than the original plasma density $n_0$.
\item
The current sheet becomes tearing unstable for sufficiently large $A$.
In the limit of $A\rightarrow\infty$ ($B_0\rightarrow 0$) the packet collision setup becomes the standard configuration for reconnection of $\pm B_y$, with no cross-layer field $B_x$.
Then, energy release is driven by the tearing instability.
It proceeds with a smaller rate $v_{\rm rec}\sim 0.1 c$ (instead of $c$) and the energized particles are ejected in plasmoids along $\pm y$, i.e. along the current sheet (instead of spreading into the upstream along $\pm x$).
Reconnection dissipates $\sim 0.2$ of the energy of the colliding waves.
\end{enumerate}

The collision of Alfv\'en waves with amplitudes $A>1/2$ in a plasma with $\sigma_0\gg 1$ provides an extremely fast and efficient dissipation mechanism.
In particular, for $A=1$ the entire wave energy converts to heat in one light-crossing time of the packet, $\lambda/c$.
This mechanism can operate in strongly perturbed magnetized plasmas around compact objects, including jets from black holes, coronae of accretion disks, magnetospheres of neutron stars, and pulsar winds.
It occurs significantly faster than magnetic reconnection or
the turbulence cascade to a small dissipation scale.

Our kinetic simulations and the analytical description of wave collision neglected radiative losses of the accelerated particles.
The losses are unlikely to reduce the dissipation efficiency or change the collision picture with the current sheet, but can change the particle trajectories in the sheet.
In particular, for waves colliding in a neutron star magnetosphere, synchrotron losses will limit the excitation of ultra-relativistic gyration in the current sheet.
Furthermore, Compton scattering will generate energetic photons which convert to $e^\pm$ pairs.
These radiative processes will occur similarly to those in radiative magnetic reconnection \citep{2020arXiv201107310B} and generate a powerful X-ray burst with a similar spectrum.

Alfv\'en waves excited at larger distances from the compact object (e.g. in a magnetized jet from a black hole or in a pulsar wind nebula) may dissipate with less severe radiative losses and with no $e^\pm$ creation.
They can still produce observable gamma-ray flares, similar to magnetic reconnection invoked previously to explain blazar flares \citep[e.g.,][]{2009MNRAS.395L..29G}.

\bigskip

\acknowledgements
X.L. is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), funding reference \#CITA 490888-16 and acknowledges the support of computational resources provided by Compute Ontario and Compute Canada.
Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities.
A.M.B. is supported by NASA grant NNX~17AK37G, NSF grant AST~2009453, Simons Foundation grant \#446228, and the Humboldt Foundation.
L.S. acknowledges support from the Sloan Fellowship, the Cottrell Scholar Award, NASA 80NSSC20K1556, NSF PHY-1903412 and DoE DE-SC0021254.

redpajama_set_name: RedPajamaArXiv


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That precedes God's vast supply.
Who perceives man's needy state.
That He freely gives His own.
Through the soul that once was dry.
"Behold, I will do a new thing; now it shall spring forth: shall ye not know it? I will even make a way in the wilderness, and rivers in the desert."


Few things are more frightening than finding yourself in an unfamiliar situation — especially if it involves the law. If that is the situation you're in now, it's important to know that there is help available.
I have years of experience helping people just like you find the legal answers they need. Because I am familiar with the courts and judges in San Francisco, I can help prepare you for every step of the real estate process. I understand the nuances of our legal system, so I can help you proactively manage any weak spots in your case and emphasize the strengths.
When you contact my firm — Hanson Law Firm — you will work with me throughout the process. I can give your case the personal attention it needs to help you meet your legal goals. Contact me or call 877-545-6738 to schedule your initial consultation.
I know that no two cases are exactly the same, and the specifics of your case will be different than the details of other people's cases. However, it may comfort you to know that there are other people who have been in situations similar to yours.
I will regularly post stories about real estate law matters, talking about things that happened here in San Francisco as well as stories from across the country. That I posted a story is not an indication that I am handling that case; however, it can help give you an idea of the types of cases I handle and the options that may be available for you.
If you are interested in learning more about the options available in your situation or you want to ensure your rights are protected, it may be beneficial to talk with an experienced real estate law attorney. To schedule an appointment, contact me online or call 877-545-6738.


text:
« TAXPAYER'S PROFILE – SECTION 114A OF THE INCOME TAX ORDINANCE, 2001 – PRESCRIBED FORM IS STILL AWAITED
Ufone ends 2020 on a positive note with a reaffirmation of its commitment to prioritize its customers »
Master Guarantee Agreement signed between Credit Guarantee Trust for Low Income Housing and Partner Financial Institutions
By Kazim Raza Rizvi | 28-Dec-2020 - 6:16 pm | 28-Dec-2020 Top Stories
A Credit Guarantee Trust, with Pakistan Mortgage Refinance Corporation (PMRC) as Trustee, has been set up by the Government of Pakistan with the support of State Bank of Pakistan (SBP) and funded by the World Bank. In line with Government's vision to promote affordable housing specially for the low- and informal-income segments, the Credit Guarantee Trust will provide risk coverage of up to 40% to primary mortgage financiers on first loss basis. The guarantee will partially alleviate the credit risk of primary mortgage financiers and provide a conducive environment for banks to finance housing for the low-income. Keeping in view the dynamics of mortgage market and to facilitate market growth, the scheme has been designed for both conventional and Islamic banks.
PMRC as trustee today signed a Master Guarantee Agreement with six leading Islamic and conventional banks including Meezan Bank, Habib Bank, BankIslami, Faysal Bank, JS Bank and Soneri Bank. This is a major step for the Government's Naya Pakistan Housing Program and making affordable housing possible for all.
Speaking at the occasion, Deputy Governor SBP Mr. Jameel Ahmed said that the risk coverage of mortgage portfolio under Government Markup Subsidy facility provides due comfort to banks in extending housing finance to the low income segment for buying or construction of new houses. He urged the banking industry to benefit from this unprecedented facilitative environment and extend loans to their maximum potential. He also urged the PMRC to focus on developing secondary mortgage market through issuance of mortgage-backed securities in the capital market. The Deputy Governor SBP emphasized that all stakeholders needed to make concerted efforts to achieve the goal of providing housing to the common people. He lauded the efforts by financial institutions over the last few months under the umbrella of Steering Committee on housing and construction finance established by State Bank of Pakistan.
Mudassir H. Khan, MD and CEO of PMRC, expressing his views said that this Credit Guarantee Scheme will pave the way for the banking industry to extend housing finance to the low income group, a market segment which has remained negligible for long. He said that PMRC has a role of a catalyst in mortgage market development in the country and for growth of affordable housing in the country. He thanked the Deputy Governor SBP for his leadership and support for this sector, the Ministry of Finance, the World Bank and NAPHDA towards making the Government and PM's vision of affordable housing a reality.
Tagged Credit Guarantee Trust, Low Income Housing, Master Guarantee Agreement, PMRC. Bookmark the permalink.


text:
Doctors in Politics
Suhas Gondi, Jonathan Kusner, and Yosef Berlyand at STAT:
Physicians do many things well. One thing they aren't good at is showing up to vote. That bad habit starts early, and we believe it can — and must — be changed.
We don't have data from recent elections, but studies from a decade ago show that physicians voted less often than the general population. (Lawyers, in contrast, were more likely to vote than the general population.) Given that health care accounts for almost one-fifth of the U.S. gross domestic product, and that new laws and regulations continuously alter the norms of medical practice, it is both curious and shameful that medical professionals fail to fulfill the basic civic responsibility of voting.
Several reasons have been tossed around to explain why physicians vote at such low rates. One is that doctors are so busy that it's difficult to fit a trip to a polling place into an already packed day. Another explanation is that some physicians decide that the value of their single vote is too small to justify taking time away from patients in need. Low voting rates could also be part of broader disengagement from public life, consistent with evidence that physicians volunteer less often than other highly educated professionals and are less likely to donate to candidates.
But now more than ever physicians need to vote because the outcomes of elections are increasingly affecting their patients and their ability to care for them. Realizing this, many have called for more doctors to get politically involved. Although we've seen in recent years a swelling of physician advocacy on political issues, from repeal and replace the Affordable Care Act to "Dreamers" to gun violence, this engagement has largely taken the form of protests, marches, and social media campaigns. Far less energy has been invested into boosting the number of doctors who cast votes, the most fundamental form of civic engagement.
Labels: government, health, health care, interest groups, political participation, political science, politics, turnout


Farrah's soft flame baked flour tortillas filled with tasty chicken, capsicum and onion cooked in a mild spice mix of cumin, smoked paprika and other tasty herbs and spices. Roll them up and drizzle over the sauce for a winning family fiesta!
Wheat flour, water, vegetable oil [with antioxidant (307)], dextrose, salt, emulsifier (471), rice flour, raising agents (500, 450), preservatives (282, 200), acidity regulator (297), stabilisers (466, 415), enzymes. Contains gluten. This product is manufactured on equipment that also produces product containing soy and sesame seeds.
Tomato (77%), onion, green pepper, cider vinegar, garlic, canola oil, corn starch, sugar, salt, chipotle, spice, herb.
Spices (28%) (cumin, coriander, smoked paprika, black pepper), rice flour, tomato, sugar, sea salt, maize flour, worcestershire sauce powder (maltodextrin, vegetable protein extract, vinegar, molasses, spices, vegetable oil), garlic, onion, natural flavours, parsley, citric acid, hickory smoke flavour.
Mexican food is a guaranteed success in our house. In particular, fajitas are always bound to please, with each family member being able to fill wraps with their favourite combination of ingredients. However, with a newborn and a toddler, as well as general day-to-day life, we have been seriously lacking in time, particularly for cooking. That is why, when these Farrah� ™s fajita meal kits came up for review, I couldn� ™t resist the chance to give them a try.
The kit contains all of the spices and sauce which you need to create a beautiful meal, alongside the tortilla wraps to contain them. All that you will need to add your meat of choice, veggies and salads. The kit box itself is really helpful, giving a suggested recipe to follow, and all of the ingredients which you need to prepare it. If you picked this up at the supermarket it would be really easy to know exactly what you needed to make your quick weeknight dinner.
When you open the pack, the contents are all well labelled and easy to use. The tortillas, as you would expect from Farrah� ™s, are so soft and will not crack, no matter how tight you roll them (my daughter tested this very well!). Using the spice mix and sauce is really easy. We chose to use them with chicken, veggies and some salads using the recipe from the back of the pack. The result was delicious - a family-friendly level of spice, but huge flavour. Our whole family approved of the wraps, and even went back for seconds of the veggies which was quite a revelation. The portion sizes allowed were generous, and plenty to feed our hungry family, as well as having leftovers for lunch the next day.
Overall, these kits are fantastic. The exceptional level of quality which you expect from Farrah� ™s, with a delicious taste which will leave the whole family coming back for more. The price, for the convenience and time-saving afforded, is fantastic, and the portion sizes are very generous. Overall, we loved this kit, and we will definitely be using it again. A fantastic product for a delicious, fast and family-friendly Mexican feast. Farrah� ™s have once again created a product which makes Mexican accessible for everyone - well done!
I was so excited when these arrived in our review pack, as my family is a huge fan of wraps, and it had been a particularly busy day so the task of not needing to worry about what to cook for dinner was greatly appreciated! The meal kit has a lovely coloured picture of the intended meal that looks delicious, so our hopes were high for a yummy meal.
Miss twelve volunteered to take task of preparing the meal, and she hunted through the fridge for the right ingredients, we had chicken breasts ready to go, and then she substituted a few things, courgettes instead of peppers, and she added in some tinned tomatoes.
One of the first things I noticed was the ease that she had in preparing and cooking the meal, it was a quick, healthy and delicious dinner, that was 'child's play'. I asked her for her feedback and she told me, these were very quick and easy to make, and they tasted so good. This was a sentiment that the whole family echoed, "these taste really good!" Half the family used the sauce, and half didn't, and this was one of the things I liked about this kit, it was easy to personalise it to each person's taste preferences.
The packs have a generous amount of spices in them, we found we only used half, and this meant we simply needed to purchase another pack of Farrah's wraps for a second delicious dinner. The second time we made these we followed the recipe and it was another tasty meal, that was simple to prepare. These meal kits are a brilliant meal base, there is no need to be bound by the recipe, we had great results with 'what we found in the fridge' as well as when we followed the recipe, wraps offer an almost endless list of meal possibilities.
We haven't tried these with steak yet, as we are more of a chicken family, but my eldest daughter is a vegan, and she has tried these with vegetables only, and she was delighted that she could purchase a meal kit that is suitable for vegans. I will definitely be recommending these to other families to have in the pantry as a staple, as a go to, easy, and healthy meal, which also full's up a hungry family.
Any meal that can be on the table with in half an hour is a winner in my eyes. We are all over the place at the moment with after school activities, Christmas parties, end of school functions and just the busyness of the season that leaves me on some days not knowing if I am coming or going. Meals seem to be a blur as they need to be fast and on the table in the blink of an eye. The past two nights we have not eaten till 8pm which is a huge issue when you have a 9 year old and a 7 year old. So tonight after ballet class we decided to put this to the test.
My youngest daughter is on a huge Mexican kick as her class room is learning about the country as there in class topic. They have a young man from Venezuela in the class and they have been learning about his country and Mexican food. When I told her we were having this she squealed in delight and asked if she could help make it.
Actually the preparation is rather simple that realistically her and her sister could probably make it without much help. Dice the chicken up and then place in a bag and coat with the Spice Mix. Fry in a pan and then add the onions and capsicum. Next heat the Tortillas on the grill to give that nice brown mark. Then make a quick salsa with red onion, tomato and avocado and grate some cheese and its basically made. Place all the ingredients in the wrap and add some sour cream and the Fajita Sauce and stand back and admire your work. Extremely simple!
With eight Tortillas in the kit it works out two a person and I found them to be extremely filling. Everybody really enjoyed them and we all agreed we would happily have again. It was nice and easy and very fast and if I got both of the girls helping me next time I am sure we could probably do much quicker. I am not usually one for the sauce they put in the boxes but I found I did enjoy this sauce and did not mind the spice to it. I also liked that the wraps stay intact and do not crack or break as your twist and fold them. A nice alternative to Nachos or Taco and something I am sure we will be having again in the very near future.
Ever since I can remember I have always enjoyed Mexican cuisine, especially enchiladas and fajitas. I like how Mexican food uses lots of spices to tantalize the taste-buds, and generally the meal lets each individual customize their meal to their own flavour preference.
Before joining KIWIreviews I was aware of the brand Farrah's, but honestly hadn't used many of their products. Since becoming an active reviewer and requesting products, Farrah's has quickly become a favourite company. I saw a new Farrah's meal kit was available to request, I quickly put my request in and crossed my fingers, to my relief I was lucky enough to receive a kit.
The appearance of the box is very striking, the bright orange really catches your attention. The box states that the kit makes 8 fajitas and was a mild spice, the serving suggestion looks mouth-watering.
When it came time to make dinner I had decided that I would use mince instead of chicken, because I had forgotten to buy chicken on the groceries. I started by reading the directions on the back of the box, I proceeded to coat the mince with some oil and the Fajita Spice Mix. The aroma that wafted up to my nostrils once the mince started cooking was scrumptious. The meat didn't take long to cook so I added my red onion and red capsicum and cooked through. After a few minutes when it was ready, I removed the mixture from the heat and started to heat up the tortillas, I found that it did not take very long for the tortillas to start to change colour, at one point one got a large bubble. Once all 8 had been heated I started to assemble the fajitas.
For each fajita I placed a tortilla on a plate, placed a generous amount of the meat and vegetable mixture on top, I then sprinkled some grated cheese on top, and finished with some of the Fajita Sauce. On the box there is a statement saying the tortillas 'won't crack, or split when rolled' I was skeptical especially when it came time to roll up. I didn't need to worry as these tortillas are some of the strongest I have used. After my first mouthful I was sold on how good this kit is, the tortilla is the right thickness and doesn't taste floury, the mince mix was a good level spiciness and my children enjoyed it too.
I recommend this kit to lovers of Mexican or spicy food, this kit is fantastic for a quick, no hassle meal. I will be purchasing more of this product in the future, and recommending to family and friends.
Our family love mexican food and will have something mexican style most weeks whether it be tacos, or nachos, or enchiladas there will be something on the weeks menu. Fajita's are something I have tried when eating out but never made myself at home. The spices from what I remember are similar to that of burritos but with a milder flavour and a great salsa style sauce. I was excited to receive the kit to see just what they would taste like making them at home.
When I opened the meal kit I was disappointing to find that I had not received the fajita spice mix, the box only contained the wraps and the fajita sauce. I had been checking out the packaging before opening so know it was completely sealed before I had opened it so the fajita spice had been missed out of the packaging during production. I managed to find some ideas for a spice mix by reading the ingredents list on the box so made a basic mexican spice mix myself to use with the chicken so probably not a completely authentic fajita spice.
As with other farrah's meal kits the instructions are simple and clear making the meal kits a great choice for an easy no fuss dinner for a busy family. The wraps as always are fresh and soft so don't tear when you wrap them with the fillings. They are smaller wraps than what you get in the individual packets of wraps but a good size for sharing dinners like fajita's. I loved the meal suggestions on the packaging to change things including a beef option and some extra condiments like guacamole and sour cream. I would defintely buy another kit to try the other options!
I think the kits are a good price as you only need to buy the meats and salads to have a complete meal although some weeks unfortunately for us this would be out of price range as buy the time you buy the extras its a $20 plus meal.I would definitely buy in future and have bought others in the farrahs meal kits range, they are a good quality kit with a much better flavour than other brands. I also love that they are NZ brand and use natural ingredients.
Farrah's Mexican Fajita Meal Kit was a hit in the household and everyone commented about how amazing tea was and if we can have it again. I was excited when I got my KIWIreviews box and seen this as I had chicken out for tea but I was not sure what I was going to cook with it. So it was prefect timing when this showed up. My son asked me if he could help and he said it was really fun to make, he helped with cutting the veges and also shaking the chicken and mix in the bag which smelt amazing the flavouring.
We added a bit of extra vegetables like mushrooms an radishes. I put all the chicken in the pan and cooked it half way through and then added the veges on top. I loved the smell it brought to the kitchen. Once this wad all cooked I cooked of the wraps for ten seconds on each side. I also made a avo and tomato salsa and also sour cream with coriander. I laid some chicken and vege mix on the wraps with some avo and tomato salsa and also sour cream and wrapped them up. We all had one each and went back for seconds. The boys went back for thirds.
I will be buying this again for the family and we will be telling friends about the yummy product as well. It goes down a treat and is so quick and easy to make. I love this and the price is great as well. Quick easy cheap and yummy what more could you ask for.
I love strong flavours. If there is a spice packet, I will use it all. If there is a sauce packet, I will use it all. If I have a wrap, I will pack as much inside as possible. For those reasons, the Fajita meal kit is not the best product for me. The amount of portion control needed here is quite major. Using the 450 grams of sliced chicken breast recommended, I ended up using all of the Fajita Spice Mix, and all of the sauce mix, and only ended up with 2 Fajitas out of it (so I still had 6 flour tortillas left at the end, but no more fillings).
The product is easy to create. Coat chicken in fajita spice mix, cook, add vegetables, then put in a tortilla and cover in sauce. Straight forward and takes minimal time to prepare. In that regard, the product is great. I would actually like the see the fajita spice mix and fajita sauces sold separately, so that I could have greater control over portion sizes, and wrap types and quantities. The 8 tortillas don't come in a resealable packet so they really are designed to be used all in the one meal, which as a single male (albeit a large overeating one) means I end up with these extra bits which I have to find another use for. Even if I did have portion control, the product is not suited for me as neither the sauce nor spices come in resealable packs either, so you have to use it all at the same time again. This is a meal that you would need multiple people looking for a snack.
For what is there, the product is easy to use, and all of the packs are easy to tear open. The heat of the spices is mild, as is advertised on the front of the pack, and the flavours were delightful. I'm not really a fan of capsicums (in fact I detest them), so instead of capsicums, I used a bag of frozen vegetables, which included onion carrots and courgettes. Still, the meal was delicious. In all honestly, the sauce is a little overpowering, and the rich tomato flavour does take over the fajita spices, but one could argue that if capsicums were actually used, that that flavour would balance better with the overpowering tomato.
I ended up coating the remaining flour tortillas with garlic butter and light layer of cheddar cheese to create makeshift cheesy garlic quesadillas.
Much to my surprise, Miss Seven, who had arrived for a meal with her parents, absolutely loved this product. I had made a plain salad for her, but it was left untouched - I subsequently had it for my own lunch next day! I am not sure what I expected from the fajita spice flavouring, but I had assumed it would be much hotter. Instead, the mix was very mild and smooth; I could taste the coriander and cumin clearly as there were no other strong flavours to overwhelm them. As I love both these spices I was very happy about that. As for the tomato sauce, that too was mild - the predominant taste was tomato, and from the low acidity I suspect it was Roma variety or something similar.
To ensure that everyone got as much or as little of each ingredient as they wished, I served up two tortillas for each of the adults with their own bowls so they could build their own. I had precooked chicken breast with the contents of the spice packet and some chopped red onion, reheated it just before serving, and divided it between the six warm tortillas. My plan was to do something else with the remaining two tortillas. Each person also got three bowls with sauce, sliced avocado, and a mixture of refried beans and whole kernel corn. Having made up our wraps, we started to eat - but Miss Seven wanted to taste her mother's. That was unfortunate; we all had to unwrap our tortillas again and spoon some chicken mixture into a spare wrap for her!
The quantity was perfect. Two each was just right for the three hungry adults while Miss Seven managed to finish hers, having done the rounds of all our bowls so she could try the extras! The consensus was unanimous; everyone enjoyed them, and they went home armed with the empty cardboard box so that they could buy them again - that was Miss Seven's idea! Apart from anything else, she loves the idea of finger food which can be eaten informally, and she declared that she was going to cook them herself once they had purchased their own packet.
Next day, I had one leftover tortilla instead of the two I had planned for, but luckily I had Miss Seven's discarded salad as well! I toasted the tortilla on both sides over a hot pan, and then served it with scrambled egg on top. There was a small amount of tomato sauce left so I decorated the egg with that. With the salad, that made a very tasty lunch. I normally serve scrambled egg on toast, but the tortilla base was delicious and something I would do again.
I will buy this product again although I would like to see the tortillas in a resealable inner bag so they stay fresh. My single tortilla was still fresh next day but as the bag had been opened I am not sure how long it would stay that way without drying out. For two of us I would probably halve the quantities and store the remainder of the spice packet and the tomato sauce in sealed boxes in the fridge, but I have successfully stored other Farrah's wraps for some time in their own bags. For the times when there are just two of us for dinner, this would be useful.
Mild, slightly sweet cheese dusted in sea-salted superfood - dried Wakame kelp flakes.


text:
Emory Miller: Blazing a trail
By Colleen O'Hara
Feds learn value of continuing ed
Training and educating the information technology workforce have taken on a new sense of urgency as procurement and management reforms place new demands on IT professionals.
Business and project management know-how have become sought-after skills, especially if those skills help agency officials keep their IT programs off the Office of Management and Budget's high-risk list.
The foundation for many of today's training programs was an innovative program called Trail
Boss that began in the late 1980s to bring together IT executives looking to share ideas and network with their peers.
"Trail Boss was probably one of the government's most successful programs because it answered a critical need when government was struggling with acquiring large mission-critical systems," said Emory Miller, a former General Services Administration executive now with Robbins-Gioia LLC. "Based on my experience, it was probably one of the broadest programs we had in training up until that time."
But even successful programs run their course. In 1999, Trail Boss made way for a new training program called the Strategic and Tactical Advocates for Results (STAR) program. STAR put in place a seminar program aimed at mid-level IT executives.
Reflecting the trends in government, STAR made project management a central part of the curriculum, Miller said. For IT managers to be successful, they have to have a broad perspective, ask intelligent questions and understand how multiple factors influence the decisions they make, he said.
In the case of chief information officer training and education, a government/university partnership filled the void. CIO University is a virtual consortium of universities offering graduate-level courses for senior executives. "We said, 'Here is what a CIO organization needs in terms of competencies to be successful,' " Miller said. "For the first time we were able to identify things most important to us, and the universities were able to respond with offerings directly addressing those issues."
Programs such as CIO University reflect the role of IT executives. They are really an "attempt to recognize there is a management level of IT that goes beyond technical infrastructures to focus on how to make IT a partner in mission delivery," said Fred Thompson, a former Treasury Department official and now a director at Unisys Corp.


International Line Builders, founded in 1983, provides a full spectrum of electrical construction services, from transmission, distribution and substation work to inside electrical construction in numerous market sectors.
We specialize in overhead and underground distribution installation repair and maintenance, along with underground drilling to provide electric power line services. Through our division, ILB Electric, we also provide commercial electrical construction services, providing our customers with a complete package of construction services under one roof.
We have locations in Tualatin, Oregon; Newman Lake, Washington; Nampa, Idaho; and Corona, Riverside and West Sacramento, California. We are a preferred contractor in many of our markets, which means you can rely on us to get it done right the first time.
International Line Builders was created in 1983 by a lineman, Marley D. Martin. Just over a decade later, MDU Resources Group, Inc. bought International Line Builders to form its new subsidiary, MDU Construction Services Group.
Today, we are a full service electrical construction company. We're still run by a team of linemen, electricians and industry experts. Throughout the West, we take care of our customers so they can take care of theirs.
International Line Builders is part of MDU Construction Services Group, Inc. With more than 5,500 skilled employees across the country and authorization to work in 43 states, MDU Construction Services Group provides industry-leading construction services. Our diverse group of companies constructs and maintains electric and communications lines, gas pipelines, fire suppression systems, and external lighting and traffic signalization. We also provide expertise in utility excavation and inside electrical and mechanical services, and manufacture and distribute transmission line construction equipment and supplies.
MDU Resources got its start as a small electric utility company in 1924 and has grown into a multi-billion dollar company whose diverse holdings, growth strategy and commitment to integrity have allowed it to consistently post strong earnings and earn the reputation of providing superior shareholder value. The company is headquartered in Bismarck, North Dakota, and has been traded on the New York Stock Exchange since 1948 under the symbol MDU.
Our mission is to seek safety on the job, quality for our customers and integrity everywhere we go. That means we're focused on the future, our customers and our people — setting the standard for industry excellence.


Elijah and Paul, from Fishing Montana channel, headed out to the incredible East Rosebud Lake for some fishing Friday and it did not disappoint!
How To Find Those Larger Female Bass?
Uncle Catfish and the rest of Rut and River Pursuit Podcast guys fishing Lake Meade in Pennsylvania.
Josh Taylor spent the day out on the water and looked at how Deeper performs in a variety of conditions.
On a hot day Paul and Elijah (from Fishing Montana channel) went after some of the legendary trout, that swim in the depths of Martinsdale Reservoir.


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