text:
Can Autism Be Cured?
Can the Discovery of Gravity Be Attributed to Newton's Supposed Autism?
How Are BIPs Designed for Students on the Spectrum?
How Are IEPs Designed for Students with ASD?
How Are Picture Exchange Communication Systems Used in Applied Behavior Analysis Therapy?
How Can I Protect my Child with Autism from Bullying?
How Can You Tell ASD from ADD/ADHD in a Young Child?
How Do You Identify Signs of Autism in Young Children?
How Do You Know if a Child Has Oppositional Defiant Disorder or ASD?
How Does ASD Differ from Angelman Syndrome?
How Does ASD Differ from Rett Syndrome?
How is ADOS (Autism Diagnostic Observation Schedule) Used to Identify ASD?
How is Autism Diagnosed?
How is Discrete Trial Training Used in ABA Therapy?
How is Exercise Used in ABA For People with ASD
How is Functional Communication Training Used in Applied Behavior Analysis?
How is IQ Testing Handled When Working with Patients with ASD
How is Naturalistic Teaching Used in ABA?
How is Pivotal Response Treatment® (PRT) Used in ABA?
How is Play Therapy Used to Treat Autism?
Is Asperger Syndrome the Same As Autism?
Is Autism Associated with Higher Intelligence?
Is Autism Genetic?
Is Skateboard Legend Rodney Mullen Autistic?
Is the Autism-Vaccine Connection a Myth?
Use this Simple 5-Step Approach Instead of Ignoring Your Crying Child
Was Albert Einstein Autistic?
Was Forrest Gump Autistic?
Was Nikola Tesla Autistic?
What are the Behavioral Extremes Seen on the Autism Spectrum?
What are the Extremes of Intelligence Seen on the Autism Spectrum?
What are the Health Problems that Co-Occur with Autism?
What Drugs Are Used to Treat Autism?
What is ADI-R and How Does it Work?
What is a Functional Behavior Assessment?
What is an Antecedent-Based Intervention
What is an Autistic Savant?
What is Behavioral Change Technology?
What is Cognitive Behavioral Intervention in the Context of Applied Behavior Analysis?
What is Deep Pressure Stimulation?
What is Elopement?
What is Emotional Dysregulation?
What is FG Syndrome (FGS)?
What is Fragile X Syndrome (FXS)?
What is Graduated Exposure?
What is High-Functioning Autism?
What is Meant by Mainstreaming?
What is Meant by the Autism "Spectrum?"
What is Meant by Differential Reinforcement in the Context of Applied Behavior Analysis?
What is Meant by Extinction in ABA Therapy?
What is Meant by Social Narratives in the Context of Applied Behavior Analysis?
What is Meant by Visual Supports in the Context of ABA Therapy?
What is Peer-Mediated Instruction and Intervention in the Context of Applied Behavior Analysis?
What is Pervasive Developmental Disorder?
What is Prompting, and How is it Used in ABA Therapy?
What is Reinforcement and Why Is It Important in ABA?
What is Self-Management in the Context of ABA Therapy
What is Sensory Processing Disorder?
What is Social Skills Training in the Context of Applied Behavior Analysis?
What is Stimming?
What is Task Analysis in the Context of Applied Behavior Analysis Therapy?
What is the Connection Between Autism and Gender Dysphoria?
What is the Difference Between Childhood Disintegrative Disorder and ASD?
What is The Neurodiversity Movement and Autism Rights?
What is the Relationship Between Autism and Impulse Control?
What is Theory of Mind and How Does it Relate to Autism?
What Makes Autistic People So Good at Math?
Where Can I Find Free ABA Services for My Child with Autism?
Who Was BF Skinner?
Why are Boys More Likely to Have Autism?
Why Do Autistic People Have Issues with Social Skills?
Why Do Some People with ASD Have Such Difficulty Communicating?
Why is ASD Frequently Associated with Anxiety and Depression?
Why is ASD Often Associated with Aggressive Behavior?
Why is Autism So Prevalent Now?
Why is OCD so Common in Children with Autism?
Why is Routine so Important to People with ASD?
Will Having Students with Autism in My Kid's Class Impact Their Learning?
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32 Best Master's in Education Programs with an ABA Emphasis
We can't help but have crazy respect for teachers, particularly those with the insight to recognize how valuable skills in applied behavior analysis can be when it comes to managing a classroom and creating the best possible learning environment for students with special needs.
There are a number of paths educators can take when making the decision to add ABA to their list of skills, and most involve meeting the qualifications for the Board Certified Behavior Analyst (BCBA) credential through the Behavior Analyst Certification Board (BACB).
If you already hold a master's degree, then a non-degree BCBA course sequence will provide you with the extra courses you need to take the BCBA exam… But if you're still preparing to pursue a master's degree in special education or general curriculum and instruction and you're looking to focus your studies on applied behavior analysis, then there's nothing like a master's in education with an ABA emphasis to get everything you need all in one program.
When completing a BACB Verified Course Sequence (VCS) along with your master's, you'll not only satisfy state requirements for any special education endorsements that might be available to you, you'll also meet the curriculum requirements for the esteemed BCBA credential. Imagine – you could complete your graduate studies, along with the course sequence necessary to qualify to sit for the BCBA exam in a program where ABA coursework is embedded as a way to complement your teacher education.
Since our list only includes programs with a Verified Course Sequence, there's no second-guessing whether the ABA courses meet the requirements for BCBA certification. And because these programs are all regionally and/or nationally accredited, you know they'll meet state licensing and endorsement requirements too. And to make things even easier on you, you'll even find options here that are offered partially or fully online.
A chance to earn your master's degree in education and BCBA certification all in an online program or at a conveniently located campus in your area, all while you continue to work… these are the kinds of graduate programs every teacher dreams about finding.
Here they are – all 32 of them.
Of the hundreds of master's degree programs available to teachers in the U.S., we hand-picked 32 that are ideal for educators looking to integrate ABA skills in the classroom. Every program found here meets these basic criteria:
Include a BACB pre-approved Verified Course Sequence (VCS) that meets the eligibility requirements for the BCBA Exam
Annual graduate school tuition rates in-line with the national average for public ($11,303) and private ($23,919) institutions adjusted for location
Hold institutional accreditation through a regional and/or national agency recognized by the US Department of Education
Online Master's in Applied Behavior Analysis
Simmons University
MS in Behavior Analysis online
Online Master of Applied Behavior Analysis program
Regis College
Online Master of Science in Applied Behavioral Analysis
MS in Applied Behavior Analysis
Online Bachelor's or Master's Behavior Analysis Degrees and Certificates
This list features programs that our editorial staff hand selected to present as top recommendations. We believe the many aspects of a program that come together to create an exceptional student experience can't be reduced to numbers alone, so no formula was used to attempt to score or rank these programs. Instead, they represent our top picks based on a thoughtful review of the things we know mean the most to students. Each one of these programs offers something unique, and all come equally highly recommended. We stand behind the principal of editorial integrity and make these recommendations independently and without compensation.
Online Master of Arts in Special Education (Applied Behavior Analysis) online
Estimated cost per academic year (tuition + fees): $11,806 (in-state tuition available to students from anywhere in the country)
Student to faculty ratio: 23:1
Arizona State University always seems to make our lists of the best schools with ABA graduate programs. ASU master's programs are widely recognized as being among the top-tier online programs for teachers in the country. In fact, in 2017, U.S. News & World Report ranked ASU's education master's 14th in the nation. The program even offers you the flexibility of being able to jump in and get started at several points throughout the year, with start dates every couple of months.
Department of Special Education
MA in Special Education with an emphasis in autism
Estimated cost per academic year (tuition + fees): $8,350 (in-state), $15,778 (out of state)
San Diego State University has become a national leader in providing programs that prepare teachers to serve the needs of their autistic students. SDSU's MA in Special Education with the option to embed the BACB Verified Course Sequence with a decided focus on students with autism really caught our attention. The Department of Special Education even extends their OSEP grant to eligible master's program candidates in exchange for working with young people with ASD (2-year service commitment for each year of funding the student receives.)
Touro University
MEd in Special Education with an emphasis in ABA
Estimated cost per academic year (tuition + fees): $25,575
Student to faculty ratio: N/A
The MEd in Special Education through Touro is all about convenience without giving up quality and direct instructor interactions. Touro's MEd program offers a face-to-face and online blended learning format, opportunities to collaborate with partner organizations in the ABA community, and the ability to satisfy the field experience required for the BCBA Exam. Classes here meet in the evenings, usually just one or two times per week.
Greely, CO
Special Education MA – Intervention Specialist: ABA emphasis, online
Ed.S. in School Psychology – ABA emphasis, campus (NASP-approved)
Estimated cost per academic year (tuition + fees): $11,444 (in-state), $20,738 (out of state)
The MA in Special Education program through the University of Northern Colorado is offered online, yet students are closely mentored by faculty who have extensive professional field experience. Most online courses and programs are delivered by the same high-quality faculty who teach on-campus.
MEd in Special Education, ABA concentration
Imagine a highly ranked university that still manages to maintain a 1:19 faculty-student ratio. Hard to believe, but that's exactly what you get with UNF's MEd in Special Education program. Not surprising, considering UNF's strong commitment to student success.
University of Hawaii Manoa
MEd in Special Education, BCBA, online/hybrid
The MEd in Special Education through U of Hawaii Manoa features courses delivered primary online, complemented with two face-to-face meetings each semester. The online courses include synchronous class sessions in the evenings so you get to learn live from instructors in real time. We also love the major research units that are part of the program—the Center on Disability Studies (CDS) and the Curriculum Research & Development Group (CRDG).
Department of Special and Early Education
MSEd in Special Education, Specialization in Advanced Special Education Practices, ABA, hybrid (online/in-person format)
We love the MSEd in Special Education at Northern Illinois University because of its convenience and flexibility. Online classes are complemented with in-person courses and two to three in-person meetings at the DeKalb campus during the course of the program. The MSEd program at NIU provides all the flexibility of an online program along with the kind of personalized feedback and guidance that can only come from face-to-face instructor interactions.
Palo Heights, IL
MA in Special Education, Behavior Intervention Specialist
We can't help but respect the fact that Trinity Christian College has been continually ranked among the top tier colleges in the Midwest according to U.S. News & World Report. The MA in Special Education, Behavior Intervention Specialist is the only special education master's degree program in Illinois to combine the Learning Behavior Specialist II (LBS II): Behavior Intervention Specialist endorsement with a BCBA course sequence.
MA in Special Education, ABA focus area, online
Ball State University's MA in Special Education is all about convenience and flexibility with working teachers in mind. Students in this 100% online program can complete the courses at any time, provided they meet weekly deadlines and finish regular assignments. Even with courses delivered entirely online, we were impressed with the fact that students here have access to a wide array of student support services, including library service, tutoring, and technology support.
College of Education and Human Development
M.Ed. in Special Education with a Concentration in Autism Spectrum Disorder and Applied Behavior Analysis
We love the University of Louisville's five-semester cohort model comprised of no more than 20 students at a time. Students in this program dedicate about 15 hours a week to their practicum coursework throughout the five-semester period. This school also earned a spot on our list because of its commitment to partnerships with ABA providers in the community, giving students access to opportunities to learn and network.
Thibodaux, LA
MEd in Curriculum and Instruction-High Incidence Disabilities with ABA option
The MEd in Curriculum and Instruction-High Incidence Disabilities with ABA option through Nicholls State University is designed for practicing educators looking to take their careers to the next level. Students of this program complete a field-based research seminar that provides them with an opportunity to evaluate classrooms and propose changes necessary for the improvement of student learning. This unique aspect of the program provides the kind of real world experience teachers look for in a quality graduate program.
MEd in Non-Licensure Special Education
MEd in Special Education and ABA
MEd in Autism and ABA
MEd in ABA
Endicott College offers four MEd options for teachers – and those aspiring to become teachers – in a fully online format, with no residency requirement. Endicott has made it a point to ensure the programs they offer are accessible and affordable to students throughout the country.
Department of Behavior Analysis
EdS in Behavior Analysis, on-campus, online
Student to faculty ratio: 7:1
The EdS in Behavior Analysis through Simmons prepares students to become leaders in the classroom. If you're ready to make a difference in the lives of students with special needs, you can be sure you'll be well prepared to implement individualized education plans based on time-tested ABA principles and methods after completing Simmons' EdS in Behavior Analysis. Simmons graduates have demonstrated a first time pass rate of 80% on the BCBA exam– 15 percentage points above the national average.
Oakland University has plenty of support services for its students, earning it a spot on our list of the top graduate programs in education with an ABA concentration. Faculty members are there to guide students throughout the program, while the combination of learning seminars, field experiences, and advanced technology help students achieve their goals. We love the MEd in Special Education, ABA concentration because it's delivered in a unique, hybrid format that allows students to engage in beneficial in-class learning while also completing convenient, online courses.
Master of Arts in Education in Behavior Analysis
Lindenwood University's MA in Education in Behavior Analysis easily earned a spot on our list of top master's programs in education and ABA. Lindenwood's School of Education has established itself as one of the most respected in the nation. With campus locations in Missouri and Illinois, Lindenwood makes earning a master's in education and ABA convenient for teachers throughout the region.
MEd in Special Education, ABA focus area
The University of Nevada Las Vegas impressed us with its autism spectrum disorder research center and clinic, something that gives students enrolled in the MEd in Special Education-ABA an opportunity to experience the application of ABA methods and principles in practice. There is nothing quite like experiential learning. Combine that with the BCBA Verified Course Sequence it includes and you got a program that has it all.
MEd in Special Education, ABA, online
Estimated cost per academic year: $9,679 (in-state), $16,411 (out of state)
The BCBA grad program in the College of Education and Human Services at Cleveland State University offers up plenty of perks, including small class sizes and a completely online delivery format. It's also part of the Center for Excellence and Innovation in Education, an outreach office of the College of Education and Human Services that supports the local community, partnering with schools in the area to provide services, resources, and collaborative learning experiences.
MA in Educational Studies, Special Education, ABA specialization
The MA in Educational Studies at OSU is a research-based program that is strongly focused on ABA. OSU's College of Education and Human Ecology provides students with many opportunities to connect with and learn from faculty while engaging in unique research opportunities. The MA in Educational Studies, Special Education, ABA specialization is no exception, providing students with a research-based course of study that is strongly focused on applied behavior analysis.
Cairn University
Master of Arts degree in ABA, online
Cairn University is a great choice for students seeking a biblically centered program designed to prepare students with both teaching skills and intervention skills based on ABA principles. In fact, it's the Christian university that offers the BCBA Verified Course Sequence with extensive autism training. There is something special about a school that gives a 50 percent tuition discount to educators working in Christian schools.
MEd in Special Education (autism track or general track), ABA
We love California University of PA's MEd in Special Education because students here enjoy no shortage of options when it comes to teacher certification programs that include the coursework you need to take the BCBA exam: elementary education, secondary education, special education, and even an endorsement in autism for those who already hold special education certification.
Mercyhurst University
MEd in Special Education and Applied Disability Studies, ABA
Mercyhurst University knows a thing or two about how to structure a program to fit the scheduling needs of working teachers. Courses in the MEd in Special Education and Applied Disabilities Studies, ABA are primarily held in the evenings, freeing up students to continue working. The program includes all the courses you need to qualify for the BCBA exam. Plus, since courses are offered year-round students have better access to the courses they want to take, allowing them to more easily custom tailor the program.
MEd in Special Education, emphasis in ABA, online
The Master of Education in Special Education at PSU is offered in a convenient and highly flexible online format, making it a smart choice for working teachers. We love its emphasis on academic and behavioral supports, preparing teachers to effectively manage behaviors and develop and administer educational assessments in the classroom and beyond.
M. S. Ed in Applied Behavior Analysis
Estimated cost per academic year (tuition): $14,817 (in-state), $20,311 (out of state)
Student to faculty ratio: 10.75:1
We appreciate Temple's commitment to accommodating the scheduling needs of teachers, offering courses in the evenings at the main campus in Philadelphia. BACB-VCS courses are even made available on-site at agencies in the community for staff and other local professionals. We love Temple's M.S. Ed in ABA for its interdisciplinary approach to teaching the principles of ABA, including two 150-hour practica as part of the program, each in a different setting.
The University of Pittsburgh's School of Education got our attention for the accolades it has received from U.S. News and World Report, which ranked it 30th among graduate schools of education. The School of Education has more than $25 million in research funding across 50 projects, so students of the MEd can feel good knowing their school makes meaningful contributions to the growing body of ABA research.
Department of Curriculum and Instruction
MEd in Special Education with a concentration in Autism and ABA
We appreciate the fact that TSU combines the fields of special education and ABA in a program that includes the courses you need to qualify for the BCBA exam. As a student of the program, you even have the option of being able to fulfill the experience requirements you need through the Texas State CARES clinic.
MEd in Special Education, ABA
The MEd in Special Education through Texas Tech University earns a spot among the best education programs in ABA for its strong partnerships with school districts, community agencies and institutions of higher education throughout the state. It's all here: The sequence of ABA courses you need for BCBA certification, and it's one of the most affordable programs on our list.
University of Houston Victoria
School of Education, Health Professions and Human Development
MEd in Special Education, ABA degree plan
The University of Houston Victoria got our attention for the flexibility it offers, giving students the choice of either completing the program online or attending class in person at the main campus in Victoria. These are the kinds of options teachers look for in a graduate program, allowing them to enjoy the best in convenience or more opportunities to participate in face to face discussions with professors and classmates. Whether attending online or on-campus, the program includes the BACB Verified Course Sequence you need to qualify for the BCBA exam.
Faculty Innovation Center
Online programs offered: Online Certificate Program in ABA and Special Education (post-graduate or for students currently earning a graduate degree)
Estimated cost per academic year (tuition + fees): $11,300 (in-state), $21,518 (out-of-state)
Entrance exam(s) required: none
The University of Texas Austin' certificate program in ABA was designed to address the growing demand for BCBAs in Texas. The number of BCBA's in Texas has more than doubled in the last two years, but even this has barely kept pace with the demand for ABA services in the state. This has sparked a need for online programs like this one, which allow students to complete an ABA course of study on their own time through convenient, online study.
University of Texas San Antonio
MA in Special Education – ABA Concentration
MA in School Psychology – ABA Concentration
MA in Educational Psychology (solely focused on behavior analysis)
We're impressed with the fact that UTSA is recognized as a Tier One research facility with more than $30 million in funding going to research taking place at the College of Education and Human Development alone. Students can be proud of the research the school contributes to gaining a better understanding of autism spectrum disorders, including important work being done in collaboration with partners in the community. UTSA's Department of Educational Psychology recently partnered with the Children's Hospital of San Antonio and the Autism Treatment Center to form the San Antonio Applied Behavior Analysis Project.
Orem, UT
We are always impressed with Utah Valley University's role as a teaching institution. The MEd in ABA program is no exception. The program places a focus on preparing graduates to serve as leaders when it comes to creating the most inclusive and effective learning environment possible for special education students.
MEd in Special Education, ABA specialization
Estimated cost per academic year (tuition + fees): $8,900
Lynchburg College made our list of the top education programs with an ABA emphasis for a number of reasons. Being recognized by the Princeton Review as one of the best colleges in 2018 certainly didn't hurt. In fact, it's one of just 16 colleges and universities in Virginia to earn the distinction of making that list. We love their MEd in Special Education with an ABA specialization because it accommodates both pre-service and in-service teachers, offering lots of research opportunities that focus on topics like autism spectrum disorders, reading disabilities, intellectual disabilities, and emotional and behavior disabilities, among others.
MA in Special Education with an emphasis in ABA
You got to love the fact that WVU offers the MA in Special Education with the BACB-verified ABA course sequence completely online, making it a clear choice for working professionals in the area. West Virginia University has earned a reputation not only for its innovative online course delivery systems, but also for its faculty members who are recognized for teaching excellence and for making important contributions to research.
All schools shown here have been contacted and informed of their inclusion on this list. Schools that do not wish to be featured are immediately removed. School names are the registered trademarks of their original owners. The use of any trade name or trademark does not imply any association with the school.
©2020 https://www.appliedbehavioranalysisedu.org All Rights Reserved.


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\section{Introduction

The Smith-Purcell (SP) radiation, observed for visible light in 1953 \cite{1953-Smith-Purcell}, has been shown to occur in a wide spectral region, from microwaves \cite{1969-Rusin-Bogomolov,2004-Grishin-Fuchs} generated using macroscopic gratings, to ultraviolet radiation \cite{2014-So-MacDonald,2019-Ye-Liu} from nanogratings.
One foreseen application of this effect would be a highly tunable free-electron light source \cite{2019-RoquesCarmes-Kooi}.
SP radiation might also be used for beam diagnostics in accelerators,
for beam position monitoring \cite{1989-Fernow, 2001-Doucas-Kimmitt,2012-Soong-Byer} or longitudinal profile characterization \cite{1997-Lampel, 1997-Nguyen, 2002-Doucas-Kimmitt, 2009-Blackmore-Doucas, 2012-Bartolini-Clarke}.
New motivation to study SP radiation comes from the development of Dielectric Laser Accelerators (DLA) \cite{2014-England-Noble,2020-Sapra-Yang}, which utilize the
inverse Smith-Purcell effect. Electron beams from DLA may in turn be used to generate SP radiation in various spectral regions.

The majority of experimental studies of SP radiation were carried out with metallic gratings. Some recent studies deal with dielectric gratings (eg.~\cite{2018-Yang-Massuda, 2019-RoquesCarmes-Kooi}); this is caused by advances in dielectric nanofabrication, improved understanding of SP emission from dielectrics, and hope that dielectrics may in some cases outperform metals in radiation intensity \cite{2019-RoquesCarmes-Kooi}.

Calculations of SP radiation intensity from gratings have a long history. Most analytical work to date considers only metallic gratings
(exception: a very simplified model in Ref.~\cite{2010-Sukhikh-Naumenko} applied to sub-THz radiation).
Ref.~\cite{2011-Potylitsyn} reviews some of the analytical models,
and their outcomes are compared in Refs~\cite{2006-Karlovets-Potylitsyn, 2016-Malovytsia-Delerue}. Many of the models build upon the seminal work by
Toraldo di Francia \cite{1960-diFrancia}, which treats both SP and Cherenkov radiation with the same formalism (``Cherenkovian effects''). The range of analytical methods include perturbative approaches valid for shallow gratings \cite{1966-Barnes-Dedrick,1973-Lalor} and
various surface current models \cite{1998-Brownell-Walsh, 2000-Trotz-Brownell, 2002-Kube-Backe, 2005-Brownell-Doucas, 2011-Potylitsyn} which are best suited for shallow gratings, but for high energies can also be applied to deep profiles \cite{1998-Brownell-Walsh}.
Most of the analytical models involve some approximations and neglect resonant cavity effects in the grating.
According to Ref.~\cite{2006-Karlovets-Potylitsyn} the results of different analytical models may differ by up to six orders of magnitude.
An exceptional position among the analytical models of SP radiation is held by the van den Berg's model
\cite{1973-vandenBerg2D, 1973-vandenBerg3D, 1974-vandenBerg-Tan}. According to the author the model is rigorous and is applicable to arbitrary grating profile. Although the model's accuracy has been questioned \cite{1998-Brownell-Walsh}, no one has explicitly shown the model to be inexact. The model does reproduce radiation intensity oscillations with increasing tooth height \cite{1998-Shibata-Hasebe}, a resonant cavity effect in the grating. However, van den Berg's approach is probably the most difficult of the SP models to apply and in the end requires nontrivial numerical calculations \cite{1973-vandenBerg2D,1994-Haeberle-Rullhusen,1998-Brownell-Walsh}.

Metals are easier to deal with in analytical models than dielectrics, because with the perfect electric conductor boundary condition it is not necessary to solve for the field inside and on the other side of the grating.
Regarding dielectric gratings, Sukhikh et al.\ \cite{2010-Sukhikh-Naumenko} report analytical calculation of SP radiation from a teflon grating, however with several special assumptions: geometry of an inverted lamelar grating (rectangular grating) with substrate thickness approaching zero, SP radiation only to one side, and neglect of secondary refractions (resonances within the grating are not reproduced); the model has been applied in \cite{2010-Sukhikh-Naumenko} for sub-THz radiation.

In recent years an increasing number of purely numerical simulations of SP radiation
were reported. Numerical simulations are equally applicable to metallic and dielectric gratings, although for a dielectric grating more time and memory resources are needed. The most common approach is a time-domain simulation; some recently used solvers are Lumerical FDTD \cite{2017-Lai-Kuang,2017-Kaminer-Kooi,2017-Remez-Shapira,2018-Massuda-Roques-Carmes} and CST \cite{2014-Liu-Xu,2015-Lekomtsev-Karataev,2017-Aryshev-Potylitsyn,2019-Zhang-Konoplev}. The time of calculation is usually from hours to days on a single CPU machine. Another approach is a frequency-domain simulation, which is much faster if infinite gratings are assumed (simulation for one unit cell with periodic boundary conditions). This approach was used in Refs.\
\cite{2018-Yang-Massuda, 2018-Massuda-Roques-Carmes, 2018-Song-Du}; however, none of these papers describes the method of simulation, and it is hard to deduce how radiation energy was calculated. A description of the simulation method can be found in papers which report frequency-domain calculations of Cherenkov radiation \cite{2018-Tyukhtin-Vorobev, 2018-Galyamin-Tyukhtin, 2019-Galyamin-Vorobev}, but these papers do not compute radiated energy.
All of the Refs. \cite{2018-Yang-Massuda, 2018-Massuda-Roques-Carmes, 2018-Song-Du,2018-Tyukhtin-Vorobev, 2018-Galyamin-Tyukhtin, 2019-Galyamin-Vorobev} use the Comsol frequency-domain solver \cite{Comsol}.

The present work focuses on frequency-domain simulation of single-electron (``incoherent'') Smith-Purcell radiation with metallic and dielectric gratings. We start in Sect.~\ref{sect-model} with a step-by-step description of calculation method for Smith-Purcell and Cherenkov radiation (``Cherenkovian effects'' \cite{1960-diFrancia}) using a frequency-domain numerical solver. Although simple in principle, the solution requires careful differentiation between phasors (as required by the numerical solver) and phasor densities (Fourier transforms) and proper interpretation of the well known expression $\Re[\frac{1}{2}\vec E\times \vec H^*]$, which is different for phasors and for phasor densities. Careful treatment leads to the solution that is correct in absolute terms, without spurious multiplicative constants. We verify our method by comparing the results for Cherenkov radiation with the exact analytical Frank--Tamm formula for radiated energy \cite{1937-Frank-Tamm,1998-Jackson,2004-Shiozawa}.

After the detailed deliberations on methodology we turn to applications. In Sect.~\ref{sect-comparison-materials} we use our frequency-domain model to compare directly radiation from gratings of fixed geometry and different materials, which to our knowledge has not yet been reported in the literature, except for the mentioned previously very limited model in Ref.~\cite{2010-Sukhikh-Naumenko}, and except for a recent paper \cite{2019-RoquesCarmes-Kooi}, which however compares theoretical upper bounds for SP radiation, not the actual computed values.
In Sect.~\ref{sect-oscillations} we demonstrate that the model captures resonant effects in the grating. While energy oscillations with increasing tooth height have been reported previously for metallic gratings \cite{1998-Shibata-Hasebe, 2014-Liu-Xu, 2015-Liu-Li,2015-Lekomtsev-Karataev}, we demonstrate them for the first time for dielectrics.
Section \ref{sect-comparison-3d-2d} briefly compares a numerical result from a three-dimensional (3D) and a two-dimensional (2D) model. This is an important issue, as the 3D models require large RAM memory and are more difficult to construct, so one usually starts with 2D modelling.
Section~\ref{sect-triangular} briefly describes radiation from triangular gratings, and Sect.~\ref{sect-summary} summarizes the paper.

In all equations in this paper we use SI units.

\section{\label{sect-model}Calculation of Smith-Purcell or Cherenkov radiation intensity with a frequency-domain solver

\subsection{\label{sect-phasors-vs-densities}Phasors vs.\ phasor densities and the expression for energy}

To perform calculations using a numerical frequency-domain solver, we must carefully distinguish between phasors and phasor densities.
In case of time-harmonic electromagnetic field we have
\begin{subequations}
	\label{eq-physical-quantities}
\begin{align}
	\vec J(\vec r,t) &
	=\Re[\vec J(\vec r) e^{j\omega_0 t}]
	=\frac{1}{2}[\vec J(\vec r) e^{j\omega_0 t}+\vec J^*(\vec r) e^{-j\omega_0 t}]
    \label{eq-pq-J}\\
    \vec E(\vec r,t) &
	=\Re[\vec E(\vec r) e^{j\omega_0 t}]
	=\frac{1}{2}[\vec E(\vec r) e^{j\omega_0 t}+\vec E^*(\vec r) e^{-j\omega_0 t}]
	\label{eq-pq-E}
\end{align}
\end{subequations}
and similarly for the $\vec B$, $\vec D$ and $\vec H$ fields.
The phasors, denoted here $\vec J(\vec r)$, $\vec E(\vec r)\ldots,$ are distinct from the temporal Fourier transforms (phasor spectral densities)
$\vec J(\vec r,\omega), \vec E(\vec r,\omega),\ldots$:
\begin{align}
\label{eq-ph-phasor-transform}
    	\vec J(\vec r,t)
	&=\frac{1}{2}[\vec J(\vec r) e^{j\omega_0 t}+\vec J^*(\vec r) e^{-j\omega_0 t}]
	=\int_{-\infty}^{\infty}e^{j\omega t}\vec J(\vec r,\omega) d\omega
	\nonumber\\
	&=\int_{-\infty}^{\infty}e^{j\omega t}
	\left\{
	\frac{1}{2}[\vec J(\vec r)\delta(\omega-\omega_0)+\vec J^*(\vec r)\delta(\omega+\omega_0)]
	\right\}
	d\omega
\end{align}
where we use a Fourier transform convention consistent with \cite{1984-Haus,2011-Schachter}.
Equation (\ref{eq-ph-phasor-transform}) implies that for time-harmonic fields, the Fourier transforms can be expressed in terms of the corresponding phasors as
\begin{subequations}
\begin{align}
	\vec J(\vec r,\omega) &= \frac{1}{2}[\vec J(\vec r)\delta(\omega-\omega_0)+\vec J^*(\vec r)\delta(\omega+\omega_0)]
    \\
    	\vec E(\vec r,\omega) &= \frac{1}{2}[\vec E(\vec r)\delta(\omega-\omega_0)+\vec E^*(\vec r)\delta(\omega+\omega_0)], \ \text{etc.}
\end{align}
\end{subequations}
Note the difference in units:
$\vec J(\vec r,\omega)\ \mathrm{[s \cdot (A/m^2)]}$,
$\vec J(\vec r)\ \mathrm{[A/m^2]}$, etc.

Maxwell equations in the frequency domain (,,time-harmonic'')
\begin{subequations}
\label{eq-Maxwell}
\begin{gather}
    \nabla\times\vec E+j\omega\vec B=0\\
    \nabla\times\vec H-j\omega\vec D=\vec J\\
    \nabla\cdot\vec D=\rho\\
    \nabla\cdot\vec B=0
\end{gather}
\end{subequations}
are valid both for phasors and for temporal Fourier transforms, and this may lead to confusion about the meaning of symbols $\vec J, \vec E,\ldots$ in a particular context.
A frequency-domain solver in engineering-oriented software like Comsol expects a phasor expression for electric current $I(\vec r)$ [A] (or current density $\vec J(\vec r)$ [A/m$^2$]), and outputs
phasors $\vec E(\vec r)$ [V/m] and $\vec B(\vec r)$ [T]. The total energy radiated through a surface is
\begin{equation}
\label{eq-W-phasors}
    W=\int_{-\infty}^\infty \int_\text{surface}
    \Re\left[\frac{1}{2}\vec E(\vec r)\times \vec H^*(\vec r)\right]
    \cdot d\vec A\,dt
\end{equation}
where $\frac{1}{2}\vec E\times \vec H^*$ is the complex Poynting vector \cite{2011-Schachter} and
$\Re[\frac{1}{2}\vec E\times \vec H^*]$ is the time-averaged power flux density $\langle\vec{PFD}\rangle$ $[\mathrm{W/m^2}]$ (in Comsol it is called ``Power flow, time average, \texttt{Poav}''). Note that for strictly harmonic fields expression~(\ref{eq-W-phasors}) is infinite.

We can ``cheat'' the solver by entering a temporal Fourier transform for current
$I(\vec r,\omega)$ instead of a phasor $I(\vec r)$, then the solver
will use the same equations (\ref{eq-Maxwell}) as for phasors to
calculate the Fourier transforms $\vec E(\vec r,\omega)$, $\vec B(\vec r,\omega),\ldots$ Now the expression $\Re[\frac{1}{2}\vec E\times \vec H^*]$ has a different interpretation and a different unit $[\mathrm{s^2 \cdot W/m^2}]$. As shown in Appendix \ref{section-derivation-W}, the total radiated energy is now equal to
\begin{equation}
\label{eq-W-transforms}
    W
    =\int_{0}^\infty
    \underbrace{
    \int_\text{surface}
    4\cdot2\pi\cdot
    \Re\left[\frac{1}{2}\vec E(\vec r,\omega)\times \vec H^*(\vec r,\omega)\right]
    \cdot d\vec A
    }_{\displaystyle dW/d\omega}
    d\omega
\end{equation}
where $dW/d\omega$ is the radiated energy per unit frequency. Here we use  only positive frequencies to allow comparison with experimental results. The numerical factor $4\cdot 2\pi$ depends on which convention for Fourier transforms is used, here it is consistent with Equations~(\ref{eq-ph-phasor-transform}), (\ref{eq-current3}), (\ref{eq-current-transform}). To obtain $dW/d\omega$ from the solver's result, take the surface integral of $\langle\vec{PFD}\rangle$ (Comsol: \texttt{Poav}) and multiply by $4\cdot 2\pi$; the result is in $[\mathrm{J\cdot s}]$ (for phasors it would be $[\mathrm{J/s}]$). Depending on the software used, the ``cheated'' solver may signal wrong units. This can be resolved by multiplying the expression for current by an arbitrary frequency range $\Delta\omega$, for example by unit angular frequency
$\Delta\omega=1$~[1/s] and dividing $\langle\vec{PFD}\rangle$ by $(\Delta\omega)^2$.

The expression $\Re[\frac{1}{2}\vec E\times \vec H^*]$ is discussed in many electrodynamics texts for phasors $\vec E(\vec r)$, $\vec H(\vec r)$, but its interpretation for transforms $\vec E(\vec r,\omega )$, $\vec H(\vec r,\omega)$ and the formula (\ref{eq-W-transforms}) cannot easily be found in textbooks. To calculate power using a phasor-based frequency-domain code, one needs to compare directly equations (\ref{eq-W-phasors}) and (\ref{eq-W-transforms}). Formulas similar to (\ref{eq-W-transforms}) appear in some papers dealing with analytical models of S-P radiation \cite{1973-Lalor, 1984-Chuang-Kong,2018-Pan-Gover}, but may be not evident to users of numerical frequency-domain codes
(for example, this issue is not addressed in tutorials and manuals of Comsol \cite{Comsol}). Ref.~\cite{2019-Szczepkowicz} presents a heuristic argument for energy computation in a frequency domain solver, which however leads to results that are too small by a factor of 4. Adding to confusion, the expression $\Re\left[\frac{1}{2}\vec E(\vec r,\omega)\times \vec H^*(\vec r,\omega)\right]$ is sometimes called ``Poynting vector in the frequency domain'' \cite{1984-Chuang-Kong}, which can easily be misunderstood as the Fourier transform of the Poynting vector (these are distinct quantities with different units, see also Appendix \ref{section-derivation-W}). Another source of confusion is that energy density may be defined on either $\omega\in(-\infty,\infty)$ or $\omega\in(0,\infty)$ -- the two definitions differ by factor 2.
Incorrect numerical factors can also arise when rivaling Fourier transform conventions from different papers are confused. All these problems call for some verification of calculated radiation intensities. This issue will be addressed in Sect.~\ref{sect-verification-frank-tamm}.

\subsection{Moving point charge -- expression for current and Floquet-periodicity}

To calculate Smith-Purcell radiation or Cherenkov radiation, we consider
a point charge $(-e)$ moving in the $\hat z$ direction with constant velocity $v=\beta c$. For a particle at $z=0$ when $t=0$ the current density is
\begin{align}
    \vec J(\vec r,t)=(-e)v\delta(x)\delta(y)\delta(z-vt)\hat z
    =(-e)\delta(x)\delta(y)\delta(z/v-t)\hat z.
\end{align}
After integration  over the transverse coordinates $x,y$, we obtain
the expression for the current
\begin{align}
    I(z,t)&=(-e)\delta(z/v-t)= (-e)\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-j\omega (z/v-t)}d\omega
    \nonumber\\
    \label{eq-current3}
    &=\int_{-\infty}^{\infty}
    \left\{\frac{(-e)}{2\pi}e^{-j(\omega/v)z}\right\}
    e^{j\omega t} d\omega,
\end{align}
so the temporal Fourier transform of $I(z,t)$ is
\begin{equation}
    \label{eq-current-transform}
    I(z,\omega)=\frac{(-e)}{2\pi}e^{-j(\omega/v)z}.
\end{equation}
This expression is input to the solver as the ``edge current''. Note that the current is a function of the longitudinal coordinate and not all of the frequency-domain solvers will allow for this dependence on position.
The current is Floquet-periodic:
\begin{equation}
    \label{eq-current-periodic}
    I(z+a,\omega)=I(z,\omega)\exp(-j k_{\mathrm F}\, a),
\end{equation}
with the Floquet vector $k_{\mathrm F}=\omega/v$. For a uniform or a periodic medium, the same spatial periodicity in the frequency domain is followed by the fields:
\begin{align}
    \label{eq-E-periodicity}&\vec E(x,y,z+a,\omega)=\vec E(x,y,z,\omega) \exp({-j k_{\mathrm F}\, a}),\\
    \label{eq-H-periodicity}&\vec H(x,y,z+a,\omega)=\vec H(x,y,z,\omega) \exp({-j k_{\mathrm F}\, a}).
\end{align}
For Cherenkov radiation in a uniform medium $a$ is arbitrary. For a non-uniform medium the Floquet periodicity occurs if the refractive index is periodic in $z$ (eg.\ an infinite grating) -- in this case $a$ must be equal to the period. For non-periodic systems (eg.\ a finite grating) Eqs.~(\ref{eq-E-periodicity}--\ref{eq-H-periodicity}) do not hold.
However, they should hold in an approximate sense near the center of a finite structure with many periods.

\subsection{Inifinte gratings -- geometry of the model}

In this paper we consider infinite gratings, periodic in the $z$ coordinate.
The described model is valid for arbitrary grating profile. We choose to focus on simple grating profiles: rectangular, and in Sect.~\ref{sect-triangular} -- triangular. As expected for numerical models, there is no additional difficulty if any other grating profile is considered, as long as the profile is well resolved by the calculation mesh (for 3D models computer memory limits may come into play).

Figure \ref{fig-grating} shows the basic grating and beam configuration assumed in this paper.
\begin{figure}
\centering
\includegraphics{fig-grating.pdf}
\caption{\label{fig-grating}
(a) Basic grating and beam configuration assumed in this paper:
grating period $a=300$~nm, tooth height $h=200$~nm,
fill factor $F=0.5$,
$\beta=0.328$ corresponding to 30~keV electrons, impact parameter $d=100$~nm. We focus on the radiation in first spectral order $m=1$. For $\theta=90^{\circ}$ the radiation wavelength is $\lambda_{\perp}=914$~nm.
(b) A 3D model with a moving point charge; the grating is infinite in the $y$ and $z$ directions.
(c) A 2D model, invariant in the $y$ direction and infinite in the $z$ direction, with a moving line charge (flat beam pulse).}
\end{figure}
The electric charge moving in the $\hat z$ direction at a distance $d$ from a grating is the source of SP radiation. In the 3D model the source is a point charge $e$, and all radiation at a given frequency $\omega$ is collected. The 2D model corresponds to the source being a line charge with charge density $e/\Delta y$, and radiation collected from a corresponding strip of width $\Delta y$. In the latter case the resulting radiated energy depends on the arbitrary transverse length $\Delta y$ -- this issue will be addressed in Sect.~\ref{sect-comparison-3d-2d}.

Figures \ref{fig-2d-model} and \ref{fig-3d-model} show the details of the model.
\begin{figure}
\centering\includegraphics{fig-2d-model.pdf}
\caption{\label{fig-2d-model} (a) A 2D infinite grating is modelled as a (b) 2D unit cell
with the Floquet boundary conditions.}
\end{figure}
\begin{figure}
\centering\includegraphics{fig-3d-model.pdf}
\caption{\label{fig-3d-model}A 3D infinite grating is modelled as a 3D unit cell
with the Floquet boundary conditions.
(a) Perfectly matched layers (PMLs).
(b) Electron path.
(c) A pair of surfaces with Floquet boundary condition.
(d) An example mesh used by a finite element method solver (Comsol).}
\end{figure}
For infinite gratings only one unit cell is needed in the calculation.
The boundaries of the calculation domain in the $\pm\hat z$ directions are connected by the Floquet boundary condition (\ref{eq-E-periodicity}--\ref{eq-H-periodicity}). Perfectly Matched Layers (PMLs) attenuate radiation in the transverse directions.
The calculation domain consists of vacuum, characterized by relative permittivity = 1, and the grating region, characterized by arbitrary complex relative permittivity $\epsilon$. Note that ``top'' PMLs are vacuum, while the ``bottom'' PMLs are grating material, see Figs.~\ref{fig-2d-model}(b), \ref{fig-3d-model}(b). This means that we model thick gratings (this case occurs more often in the experiments). If the bottom PML is changed to vacuum, a thin grating is modelled, reflections from the back side of the grating occur, and guided mode resonances occur for certain frequencies (see Ref.~\cite{2016-Szczepkowicz} and references therein), with major impact on the radiation intensity.
The 3D model is more realistic than a 2D model, but requires large RAM memory (10--20 GB); the computation time for a single frequency is of the order of minutes on a single CPU machine.
The 2D model requires much less memory and the computation time is of the order of seconds.
In the 3D simulation, radiation at a given frequency $\omega$ is collected from all transverse directions, by calculating the surface integral in Eq.~(\ref{eq-W-transforms}) over the inner boundary of the PML  (violet cylindrical strip in Fig.~\ref{fig-3d-model}(a)). In the 2D model, for a given frequency $\omega$, the integration is carried out over the planar inner PML boundary (Fig.~\ref{fig-2d-model}(b)).

We performed all calculations using the frequency-domain solver in the Comsol simulation software environment \cite{Comsol}, which utilizes the Finite Element Method (FEM). The FEM mesh is shown
in Fig.~\ref{fig-3d-model}(d). We tried various refinements of the mesh and obtained slight scatter of the computed results. On the basis of these trials we believe that the numerical values presented in this paper are accurate up to $\pm 20\%$, limited by the used hardware (20 GB RAM). Frequency-domain FEM method can also be applied to ultrarelativistic particles \cite{2020-Hausler}, but the mesh has to be refined along $z$ to account for the contraction of the electromagnetic field of the electron. We note one numerical peculiarity: in Comsol, for 3D models, the default iterative solver fails to find a solution within one hour, but if the direct solver is chosen, the solution is found within minutes.

\subsection{\label{sect-verification-frank-tamm}Verification of the model against the Frank-Tamm formula}

At the end of Sect.~\ref{sect-phasors-vs-densities} we pointed out several pitfalls that may lead to incorrect multiplicative factors in calculations of SP radiation intensity. This doesn't matter if only relative intensity is needed or one aims at order-of-magnitude estimates, but if accurate results are needed, it is best to initially test the used model against some rigorous analytical result. We propose a novel approach to this problem. We take advantage of the fact that the numerical model described above is the same for SP and for Cherenkov radiation -- the only difference is in the distribution of relative permittivity in space, $\epsilon(\vec r)$.
So for a moment we change the relative permittivity of the vacuum region to $\epsilon$ and calculate the radiated energy in the uniform medium -- the Cherenkov radiation, shown in Fig.~\ref{fig-cherenkov},
\begin{figure}
\centering\includegraphics{fig-cherenkov.pdf}
\caption{\label{fig-cherenkov}Cherenkov radiation -- visualization of the Fourier transform of the electric field, $\Re[E_z(\vec r,\omega)]$, for $\omega=2\pi\cdot4\cdot10^{14}~\mathrm{s^{-1}}$, $\beta=0.5$, $n=5$.}
\end{figure}
and compare the radiation intensity with the Frank--Tamm formula, Eq.~(\ref{eq-Frank-Tamm}) in Appendix \ref{sect-derivation-Frank-Tamm}. The results are shown in Table \ref{table-cherenkov}.
\begin{table}
\centering
\begin{tabular}{|c|c|}
 \hline
 Velocity and refractive index
 & $\left.\displaystyle\frac{\mathstrut d^2 W_\mathrm{num}}{\mathstrut dz\,d\omega} \middle/ \displaystyle\frac{\mathstrut d^2 W_\mathrm{analytical}}{\mathstrut dz\,d\omega}\right.$\rule[-3.2ex]{0em}{7.6ex} \\
 \hline\hline
 $\beta=0.33$, $n=3.6$ & 1.04 \\
 $\beta=0.5$, $n=3.6$ & 1.08 \\
 $\beta=0.5$, $n=5$ & 1.04 \\
 $\beta=0.3$, $n=2$ & no radiation \\
 \hline
\end{tabular}
\caption{\label{table-cherenkov}Cherenkov radiation -- verification of the numerical results against the Frank-Tamm formula for one frequency, $\omega=2\pi\cdot4\cdot10^{14}~\mathrm{s^{-1}}$. Here we compare the numerical value $d^2 W_\mathrm{num}/dz\,d\omega$ against the analytical value $d^2 W_\mathrm{analytical}/dz\,d\omega = (e^2/4\pi)\mu_0\omega(1-1/\beta^2n^2)$ (see Appendix~\ref{sect-derivation-Frank-Tamm}); the second column shows the ratio of these two values.}
\end{table}
The ratio of the numerical radiated energy $d^2 W_\mathrm{num} / dz\, d\omega$ to the analytical value is close to 1, within 10\%. The slight discrepancy can be reduced by refining the FEM mesh (within accessible computer memory). The parameters in the last row in the table do not fulfil the Cherenkov radiation condition (see Appendix~\ref{sect-derivation-Frank-Tamm}); in this case the calculated energy is 20 orders of magnitude lower, on the level of numerical noise of the calculation -- this is the expected result.
We also checked that the computed energy is linear in $\omega$. These results demonstrate that our model is exact, with no spurious multiplicative factors.

\section{\label{sect-comparison-materials}Comparison of radiation from metallic and dielectric gratings

We assume grating and beam configuration described in Fig.~\ref{fig-grating}(a--b), a 3D model, and calculate the SP radiation emitted within the frequency range
$2\pi\cdot 325.5\mathrm{~THz}<\omega<2\pi\cdot 330.5\mathrm{~THz}$; this corresponds to radiation emitted perpendicular to the grating within 5~THz bandwidth, into angles $88.7^{\circ}<\theta<91.3^{\circ}$; the corresponding wavelength range is $907~\mathrm{nm}<\lambda<921~\mathrm{nm}$; see the SP formula in Fig.~\ref{fig-grating}(a).

To simulate a perfect conductor, we set the relative permittivity to $\epsilon = -10000+0i$ -- large negative real part and zero imaginary part. This is based on the observation that for optical frequencies good conductors have a large negative real part of $\epsilon$
(eg.
$\epsilon(\text{Cu}) =-36.8+1.36i$,
$\epsilon(\text{Au}) =-38.4+1.46i$
at $\lambda=914$~nm
\cite{2015-McPeak-Jayanti,refractiveindexinfo}%
),
while the imaginary part of $\epsilon$ describes energy dissipation and should vanish for a perfect conductor. This corresponds to large imaginary index of refraction $n=100i$, yielding almost instantaneous decay of the field inside the material (skin depth = $0.0016\lambda $ = 1.5 nm).
We verified numerically that for S--P radiation from metallic gratings in the considered frequency range, the bulk condition $\epsilon = -10000+0i$ yields the same result as the surface PEC condition (Perfect Electric Conductor, $\hat n \times \vec E = \vec 0$); this would not be valid in the sub-THz frequency range \cite{2010-Sukhikh-Naumenko}. While the boundary condition is computationally more efficient, we choose to use the bulk condition, so that exactly the same numerical model can be applied both to metallic and dielectric gratings –- only the grating's relative permittivity $\epsilon$ is changed.

The resulting SP radiation for five materials is shown in Table~\ref{table-comparison-materials}.
\begin{table}
\centering
\begin{tabular}{|c|c|c|c|c|}
 \hline
   \multicolumn{1}{|p{7em}|}{\centering Grating \\ material} &
   \multicolumn{2}{|p{10em}|}{\centering Relative permittivity \\ ($\lambda=914$~nm)} &
   \multicolumn{1}{|p{7em}|}{\centering Radiated energy \\ $W$ } &
   \multicolumn{1}{|p{8em}|}{\centering Energy radiated into \\ the grating $W_\mathrm{in}$}
   \\
   \cline{2-3}
   &
   \multicolumn{1}{|p{4em}|}{\centering Real part \\ $\epsilon_1$} &
   \multicolumn{1}{|p{4em}|}{\centering Imaginary \\ part $\epsilon_2$} & &
   \\
 \hline\hline
  Copper & $-36.85$ & 1.361 & $4.4\cdot 10^{-25}$ J & 0 \\
  Gold   & $-38.36$ & 1.462 & $4.4\cdot 10^{-25}$ J & 0 \\
  Perfect conductor & $-10000$ & 0 & $3.1\cdot 10^{-25}$ J & 0 \\
  Fused silica & 2.107 & 0 & $4.8\cdot 10^{-27}$ J & $8.8\cdot10^{-27}$ J \\
  Silicon & 13.32 & 0.03099 & $3.0\cdot 10^{-26}$ J & $6.8\cdot 10^{-26}$ J \\
 \hline
\end{tabular}
\caption{\label{table-comparison-materials}SP radiation from gratings of different materials, emitted perpendicular to the grating within the frequency range
$2\pi\cdot 325.5\mathrm{~THz}<\omega<2\pi\cdot 330.5\mathrm{~THz}$, corresponding to angular range $88.7^{\circ}<\theta<91.3^{\circ}$,
per electron per grating period, for the grating geometry and beam parameters from Fig.~\ref{fig-grating}(a--b). Relative permittivity is taken from Refs. \cite{refractiveindexinfo, 1965-Malitson,2015-McPeak-Jayanti, 2015-Schinke-Peest}.}
\end{table}
Metallic gratings outperform dielectric gratings by 1--2 orders of magnitude in terms of radiation intensity under the conditions studied (simple rectangular grating, 30 keV electrons, radiation wavelength $\sim1$~um). This confirms expectations from comparison of theoretical upper bounds for radiation from Ref.~\cite{2019-RoquesCarmes-Kooi}
(plot of ``material factor'' in Supplementary Fig.~10).
An interesting observation is that for dielectric gratings twice more energy is radiated inside the grating than emitted as external SP radiation. It is an interesting question whether the energy radiated inside could be reflected using eg.\ a vacuum/dielectric Bragg mirror (DBR) \cite{2019-Yousefi-Schonenberger}.

Data in Table~\ref{table-comparison-materials} is a direct comparison of SP radiation from metallic and dielectric gratings, however it is only for one set of beam and grating parameters. In future work the study should be extended to other electron energies, grating configurations and radiation angles. In particular, it would be interesting to check the prediction from Ref.~\cite{2019-RoquesCarmes-Kooi} that silicon may outperform metals for very low energy electrons (below 10~eV).

\section{\label{sect-oscillations}Energy oscillations with grating tooth height -- grating resonances

Results of the previous section were for a grating with a fixed tooth height. Does the intensity of SP radiation change if the tooth height is changed? The answer is shown in Fig.~\ref{fig-oscillations-comparison-of-materials}.
\begin{figure}
\centering\includegraphics{fig-oscillations-comparison-of-materials.pdf}
\caption{\label{fig-oscillations-comparison-of-materials}SP radiation from gratings of different materials,
in the angular range $88.7^{\circ}<\theta<91.3^{\circ}$,
per electron per grating period, for grating geometry shown in Fig.~\ref{fig-grating}(a--b) (3D model).
Solid line -- numerical calculation in the frequency domain. For the metallic grating the result is compared with an analytical calculation based on Ref.~\cite{2005-Brownell-Doucas} -- dashed line.
}
\end{figure}
SP radiation intensity $W$ oscillates with increasing tooth height $h$ (the impact parameter $d$ is kept constant, see Fig.~\ref{fig-grating}). The effect is known for metallic gratings,
it has been experimentally observed in the millimeter-wave spectral region using a special metallic grating setup with variable tooth height \cite{1998-Shibata-Hasebe}. The effect has also been shown for metallic gratings in an analytical calculation based on van den Berg's model \cite{1998-Shibata-Hasebe} and in numerical time-domain models \cite{1998-Shibata-Hasebe, 2014-Liu-Xu, 2015-Liu-Li,2015-Lekomtsev-Karataev}. Here we confirm oscillations of $W(h)$ for metallic gratings in a frequency-domain simulation; in addition, we demonstrate that the oscillations also occur for dielectric gratings, see Fig.~\ref{fig-oscillations-comparison-of-materials}(b--c). An interesting result is that for all materials, the optimum tooth height is close to one quarter of the radiation wavelength in the perpendicular direction.

The $W(h)$ oscillations are of resonant nature. Similar effects for the more general phenomenon of diffraction radiation \cite{2011-Potylitsyn-Ryazanov} have been predicted for the motion of charged particles near an open metallic or dielectric resonator \cite{1981-Nosich,2019-Yevtushenko-Dukhopelnykov}
or an array of metallic resonators \cite{1977-Veliev-Nosich};
enhanced radiation occurs for frequencies close to one of the resonant frequencies of the cavity. In case of the oscillatory effect shown in Fig.~\ref{fig-oscillations-comparison-of-materials}, the cavity is formed between adjacent grating teeth. The essence of the effect is already captured by a 2D model, see Fig.~\ref{fig-oscillations-metallic-2d}.
\begin{figure}
\centering\includegraphics{fig-oscillations-metallic-2d.pdf}
\caption{\label{fig-oscillations-metallic-2d}SP radiation from gratings of different tooth heights $h$,
in the angular range $88.7^{\circ}<\theta<91.3^{\circ}$,
per electron per grating period, for grating geometry shown in Fig.~\ref{fig-grating}(a,c) (2D model) with $\Delta y=1$~nm. Grating fill factor $F=0.5$ (red) and $F=0.9$ (blue).}
\end{figure}
The green insets show the analogy with the elementary one-dimensional theory of clarinets or organ pipes, where the resonant lengths of a cavity which is open at one end, for a fixed wavelength $\lambda$, are equal to $\frac{1}{4}\lambda+m\cdot\frac{1}{2}\lambda$ (vertical dashed lines in Fig.~\ref{fig-oscillations-metallic-2d}; see also Ref.~\cite{2014-Liu-Xu}). This simple one-dimensional reasoning explains the essence of the effect, but does not explain the slight shift of the calculated radiation maxima $W(h)$ towards smaller $h$.
Note that in the acoustic case this model is also approximate.
The simple model does not work in case of dielectric cavities
-- the period of $W(h)$ oscillations in Fig.~\ref{fig-oscillations-comparison-of-materials}(b--c) has no obvious relation to the vacuum wavelength or the wavelength inside the dielectric; maybe one could deduce the effective wavelength on the grounds of effective mode index theory.

The intensity oscillations for a metallic grating can alternatively be explained by considering the groove cavity as a transmission line which is short-circuited at one end (bottom of the groove; impedance = 0) and open-circuited at the other end (top of the groove). If in the groove only the TEM mode is considered (transmission line approximation), the first resonance will occur when $h=\lambda/4$ (high impedance at the top end of the line). However, in practice many other modes must be used in order to satisfy the boundary conditions. Due to the presence of these evanescent modes electromagnetic energy is stored near the edge (top) of the groove. Effectively, this stored energy is manifested in a shift in frequency (see Fig.~\ref{fig-oscillations-metallic-2d}), since in general near an edge the magnetic energy does not equal the electric energy – as is the case in an ideal cavity or plane waves. This effect is well known in waveguide theory and it is usually described in terms of length: the electrical length differs from the geometrical length.

The van den Berg's model cannot be applied to dielectrics, but it would be interesting to compare it with oscillations shown in Fig.~\ref{fig-oscillations-comparison-of-materials}(a) for metallic grating, similarly as was done in Ref.~\cite{1998-Shibata-Hasebe}. However, van den Berg's model is not easy to apply, so instead we compare our numerical results with the analytical results of a surface current model, using expressions from Ref.~\cite{2005-Brownell-Doucas} (dashed line in Fig.~\ref{fig-oscillations-comparison-of-materials}(a)). An order of magnitude agreement is found, but the surface current model does not predict oscillations of $W(h)$. The explanation can be found in the original paper by Brownell, Walsh and Doucas:
``in deep tooth profiles several facets may form a
cavity and limit the field modes when the wavelength is
comparable to or longer than the cavity dimensions. The
model described here is best suited for shallow gratings
where cavity behavior is negligible but can be applied to
deep profiles if the energy is sufficiently high so that the
wavelength is much smaller than any cavity'' \cite{1998-Brownell-Walsh}.

\section{\label{sect-comparison-3d-2d}Comparison of 3D and 2D results for the Smith-Purcell radiation

As was shown in the previous section, certain effects in the SP radiation can be captured well within a 2D model, which is much simpler to construct than a 3D model. What about radiation intensity: can we estimate it from a 2D model? Comparison of the numbers in Figs.~\ref{fig-oscillations-comparison-of-materials}(a) and \ref{fig-oscillations-metallic-2d} reveals a difference in energy by 3 orders of magnitude. One should not expect agreement, because the two physical situations are different: single electron vs.\ an infinite line charge with linear density $\rho=e/\Delta y$. The latter contains an arbitrary parameter $\Delta y$, and the final calculated energy $W$ is inversely proportional to this parameter ($W \propto \rho^2\Delta y = (e/\Delta y)^2\Delta y = e^2/\Delta y$ -- we are grateful to Urs H\"{a}usler for pointing this out).
For Fig.~\ref{fig-oscillations-metallic-2d} the parameter $\Delta y$ was arbitrarily chosen to equal 1~nm (radiation is generated by a line of charge with a transverse charge density of $e/1$~nm; radiation $W$ is collected from a longitudinal strip of the grating of width 1 nm), a length not connected with the characteristic length scales of the considered grating/beam configuration. It appears reasonable to replace $\Delta y=1$~nm with $\Delta y=\lambda_\perp$, which is one of the characteristic lengths of the system. The result is shown in Table~\ref{table-comparison-3d-2d}.
\begin{table}
\centering
\begin{tabular}{|c|c|}
 \hline
 Geometry of the model & Radiated energy $W$ \\
 \hline\hline
 3D model & $3.12\cdot10^{-25}$ J \\
 2D model, $\Delta y=\lambda_\perp=914$ nm & $2.02\cdot10^{-25}$ J \\
 2D model, $\Delta y=1$ nm & $1.85\cdot10^{-22}$ J\\
 \hline
\end{tabular}
\caption{\label{table-comparison-3d-2d}Comparison of 3D and 2D SP radiation in the angular range $88.7^{\circ}<\theta<91.3^{\circ}$ for a metallic grating with beam/grating configuration of Fig.~\ref{fig-grating}.}
\end{table}
The 2D result now predicts the order of magnitude of the 3D result. It remains an open question whether this trick would work equally well for other beam/grating configurations.

\section{\label{sect-triangular}Metallic triangular grating (3D)

In previous sections we considered rectangular gratings. In this section we briefly consider a 3D model of a grating with a triangular profile shown in Fig.~\ref{fig-3d-model-triangular}.
\begin{figure}[hbp]
\centering\includegraphics{fig-3d-model-triangular.pdf}
\caption{\label{fig-3d-model-triangular}(a) An infinite triangular grating, 3D model. All parameters are the same as in Fig.~\ref{fig-grating}, but $h$ is varied.
(b) The unit cell for $h=40$~nm and (c) $h=320$~nm. In all cases the grating period and the impact parameter are $a=300$~nm, $d=100$~nm.}
\end{figure}
This is motivated by the expectation that the surface current model of Ref.~\cite{2005-Brownell-Doucas} should work well for such a configuration, provided that the grating is shallow, $h\ll a$, so that resonant cavities do not form. We decided to test this hypothesis. In Table~\ref{table-triangular} we compare our 3D results with the analytical result based on formulas from Ref.~\cite{2005-Brownell-Doucas}.
\begin{table}
\centering
\begin{tabular}{|c|c|c|c|}
 \hline
 Grating tooth height $h$ & $W$, numerical model & $W'$, analytical model & Ratio $W'/W$  \\
 \hline\hline
  \phantom040 nm &  $1.42\cdot10^{-27}$ J & $5.7\cdot10^{-27}$ J & 4.0\\
  \phantom080 nm &  $3.18\cdot10^{-27}$ J & $1.1\cdot10^{-26}$ J & 3.5\\
  160 nm & $4.96\cdot10^{-27}$ J & $1.2\cdot10^{-26}$ J & 2.4\\
  320 nm & $6.28\cdot10^{-27}$ J & $6.7\cdot10^{-27}$ J & 1.1\\
 \hline
\end{tabular}
\caption{\label{table-triangular}SP radiation from metallic triangular gratings, in the angular range $88.7^{\circ}<\theta<91.3^{\circ}$, per electron per grating period, for grating geometry shown in Fig.~\ref{fig-3d-model-triangular}. We compare our numerical results with the analytical model of Ref.~\cite{2005-Brownell-Doucas}}
\end{table}
Similarly as in Fig.~\ref{fig-oscillations-comparison-of-materials}(a), we obtain an order of magnitude agreement. However, contrary to our expectations, the agreement gets worse as the tooth height is decreased. We believe that this points either to the inexactness of surface current model even for shallow gratings, or to some multiplicative factor issue as discussed at the end of Sect.~\ref{sect-phasors-vs-densities}. This remains an open question, we have only checked that it is not the frequency range issue $(-\infty,\infty)$ vs.\ $(0,\infty)$, because Eqs~(14.60) and (14.70) in Ref.~\cite{1998-Jackson}, which are the starting point in Ref.~\cite{1998-Brownell-Walsh}, are for $\omega\in(0,\infty)$, same as assumed in our calculations.

\section{\label{sect-summary}Summary and conclusions}

We constructed a numerical frequency-domain model useful for quick calculations of Smith-Purcell radiation intensity from a single particle, verified its accuracy, and discussed some concrete applications. We were somewhat conservative in the choice of grating geometry (rectangular and triangular gratings of uniform material). This was a deliberate choice which facilitated comparison with the older literature. The paper in large part deals with the method, but also presents new results regarding comparison of SP radiation from metallic and dielectric gratings; the possible numerous other applications are left for future work. The main results of the paper can be summarized as follows:
\begin{enumerate}
    \item A frequency-domain numerical model offers quick calculations of SP radiation intensity (seconds for 2D models, minutes for 3D models, for one frequency, on a single CPU machine).

    \item While it is relatively easy to calculate SP radiation in arbitrary units, obtaining an accurate result in concrete units with no spurious multiplicative constants requires careful differentiation between phasors (quantities expected by the numerical solver) and phasor densities (temporal Fourier transforms). After this issue is properly taken care of, the model is simple, easy to implement, and its accuracy is limited only by the spatial mesh density, possibly limited by the amount of RAM computer memory accessible to the user.

    \item The accuracy of the numerical model can be conveniently checked against the analytical result: the Frank-Tamm formula.

    \item For 30 keV electrons dielectric gratings are less efficient in terms of intensity of SP radiation than their metallic counterpart, by an order of magnitude for silicon, and two orders of magnitude for silica.

    \item The described numerical model captures resonant effects in the grating which are not accounted for in some analytical models. In particular, both for metallic and dielectric gratings, SP radiation intensity oscillates with grating tooth height. Both for metals and dielectrics, the optimum tooth height for maximal SP radiation perpendicular to the grating is close to a quarter of the radiation wavelength.

    \item For dielectric gratings, more SP radiation enters the grating bulk than is radiated outward into the vacuum.

\end{enumerate}

\section*{Funding}

This work was supported by the Gordon and Betty Moore Foundation
(grant no.\ GBMF4744) and the U.S. Department of Energy,
Office of Science (grant nos.\ DE-AC02-76SF00515 and
DE-SC0009914). LS was supported by the Israel Science Foundation.

\section*{Acknowledgments}
We are grateful to  Avi Gover for pointing us to the older literature on the Smith-Purcell effect and for helpful comments; to  Yen-Chieh Huang, Koby Scheuer, Naama Cohen and Urs H\"{a}usler for inspiring discussions.

A.S. is grateful to the Wroclaw Centre for Networking and Supercomputing for granting access to the Platon U3 computing infrastructure.

\section*{Disclosures}

The authors declare no conflicts of interest.

redpajama_set_name: RedPajamaArXiv


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text:
Reprezentacja Rosji na Zimowych Igrzyskach Paraolimpijskich 2006 liczyła 29 sportowców.

Medale

Złote medale
 Narciarstwo klasyczne (biathlon i biegi narciarskie)
 11 marca: Rustam Garifoullin, biathlon, 12,5 km mężczyzn stojąc
 11 marca: Vladimir Kisilev, biathlon, 12,5 km mężczyzn siedząc
 12 marca: Taras Kryjanovski, biegi narciarskie, 5 km mężczyzn siedząc
 14 marca: Irek Mannanov, biathlon, 7,5 km mężczyzn niewidomych
 14 marca: Rustam Garifoullin, biathlon, 7,5 km mężczyzn stojąc
 14 marca: Alena Gorbunova, biathlon, 7,5 km kobiet stojąc
 14 marca: Vladimir Kisilev, biathlon, 7,5 km mężczyzn siedząc
 15 marca: Anna Burmistrova, biegi narciarskie, 10 km kobiet stojąc
 15 marca: Taras Kryjanovski, biegi narciarskie, 10 km mężczyzn siedząc
 15 marca: Lioubov Vasilieva, biegi narciarskie, 10 km kobiet niewidomych
 17 marca: Irina Polyakova, Lioubov Vasilieva, Tatiana Iljutsjenko, biegi narciarskie, sztafeta 3x2,5 km kobiet
 19 marca: Kirill Mikhajlov, biegi narciarskie, 20 km mężczyzn stojąc
 19 marca: Lioubov Vasilieva, biegi narciarskie, 15 km kobiet niewidomych

Srebrne medale
 Narciarstwo klasyczne (biathlon i biegi narciarskie)
 11 marca: Alfis Makamedinov, biathlon, 12,5 km mężczyzn stojąc
 11 marca: Irek Mannanov, biathlon, 12,5 km mężczyzn niewidomych
 11 marca: Taras Kryjanovski, biathlon, 12,5 km mężczyzn siedząc
 12 marca: Anna Burmistrova, biegi narciarskie, 5 km kobiet stojąc
 12 marca: Tatiana Iljutsjenko, biegi narciarskie, 5 km kobiet niewidomych
 14 marca: Anna Burmistrova, biathlon, 7,5 km kobiet stojąc
 15 marca: Alfis Makamedinov, biegi narciarskie, 10 km mężczyzn stojąc
 15 marca: Sergej Sjilov, biegi narciarskie, 10 km mężczyzn siedząc
 15 marca: Tatiana Iljutsjenko, biegi narciarskie, 10 km kobiet niewidomych
 17 marca: Sergej Sjilov, Irek Mannanov, Rustam Garifoullin, 1x3,75+2x5 km biegi narciarskie, sztafeta mężczyzn
 18 marca: Taras Kryjanovski, biegi narciarskie, 15 km mężczyzn siedząc
 19 marca: Anna Burmistrova, biegi narciarskie, 15 km kobiet stojąc
 19 marca: Alfis Makamedinov, biegi narciarskie, 20 km mężczyzn stojąc

Brązowe medale
 Narciarstwo klasyczne (biathlon i biegi narciarskie)
 11 marca: Mikhail Terentiev, biathlon, 12,5 km mężczyzn siedząc
 12 marca: Lioubov Vasilieva, biegi narciarskie, 5 km kobiet niewidomych
 14 marca: Elvira Ibraginova, biathlon, 7,5 km kobiet niewidomych
 15 marca: Kirill Mikhajlov, biegi narciarskie, 10 km mężczyzn stojąc
 15 marca: Valeri Kouptsjinsky, biegi narciarskie, 10 km mężczyzn niewidomych
 18 marca: Sergej Sjilov, biegi narciarskie, 15 km mężczyzn siedząc
 19 marca: Tatiana Iljutsjenko, biegi narciarskie, 15 km kobiet niewidomych

Linki zewnętrzne
 ZIP 2006 w Turynie na stronie Międzynarodowego Komitetu Paraolimpijskiego

Państwa uczestniczące w Zimowych Igrzyskach Paraolimpijskich 2006
Rosja na igrzyskach paraolimpijskich
2006 w Rosji

redpajama_set_name: RedPajamaWikipedia


I recently ate dinner at BurgerFi in Downtown Delray Beach. This fast food burger chain reminded me of a modern version of Five Guys with a better menu.
I had a strawberry milkshake as my drink. It came topped with whipped cream and sprinkles. For almost $5, I thought it was somewhat expensive for the size cup the milkshake was served it. Tasted good though.
Fries and onion rings. The onion rings were good, but the fries were very average.
I had a Chicago Style Chicken Apple Sausage. The sausage was served on a poppy seed bun, topped with tomato, onions, relish, peppers, and a pickle slice. BurgerFi was generous with the toppings, but I was expecting something a little different with the sausage itself. I couldn't detect any sort of apple flavor and the sausage tasted like a normal hot dog to me.
Overall, the food was pretty average at BurgerFi. I wouldn't purposefully rush back any time soon, but it definitely was better than Five Guys (I don't get the appeal of that place) and other similar burger chains.
I wasn't impressed the first time I was here. I ordered the Meatball Pho and the broth was very bland. The beef broth in pho is normally really flavorful, but in this case I had to add lots of condiments to give it some more taste. The meatballs weren't much better, tasting much better after being dipped in some hoisin or sriracha. For a restaurant that claimed to be award winning, I was disappointed.
A few months later, I decided to give Anh Hong another try. I forget the exact name of the dish that I ordered, but according to some of the online menus I found, I had the Cho Lon Combo. This was a big bowl of egg noodles, topped with shrimp, squid, crab meat, roast pork, assorted greens, jalapenos, and lime slices. A bowl of broth was served on the side. I'm not sure the proper eating technique of getting the broth on the side like this, but I ended up pouring it over everything in my larger bowl. Unlike my first soupy experience at Anh Hong, the food tasted much better this time around. The broth had lots of flavor, the meats were cooked to perfection, and was overall good.
Green Day Cafe is a healthy, eco-friendly fast food restaurant on Lee Road in Orlando in an old Taco Bell building. I was intrigued by the concept when I first heard about the restaurant but really didn't think they would last. Green Day Cafe is still open after a few years since I first noticed them, so I decided it was about time to taste their eco-friendly food.
I had their 7-Layer Rice Bowl (Green Day Cafe is in a former Taco Bell building. My menu item of choice at Taco Bell is a 7-Layer Burrito, and I ordered a 7-Layer Rice Bowl here!). This large portion of brown rice was topped with black beans, colby jack cheese, guacamole, salsa, hummus, and buffalo sauce. While a couple of the ingredients didn't seem to go with the others (hummus), it still tasted good. The buffalo sauce/salsa gave the bowl a nice bit of spiciness and guacamole is good with everything. Who knows if this rice bowl was actually healthy by the time they put on all of the sauces, but I suppose it is definitely better for you than eating a burger.
I'd return to Green Day Cafe.
I read about Kingfish Bistro in an Orlando Weekly article. According to the article, they are apparently a Vietnamese owned Italian restaurant, and that combination intrigued me. Because of this, Kingfish was dinner last time I was in College Park. There wasn't really too much Vietnamese-Italian fusion food going on here. The majority of the menu seemed strictly Italian, except for several out of place items, such as these egg rolls that we had for an appetizer.
We also decided to share a half meatball, half cheese pizza. The pizza was good, although not great. It was comparable to most of the other nearby pizzerias which are all pretty much middle of the road and average in this neighborhood. I'd have Kingfish's pizza again if I was eating there, but I wouldn't seek it out to fulfill any sort of pizza cravings.
Overall, the food at Kingfish Bistro was good, although not great. I liked the egg rolls as a prelude to pizza, but I really would have liked to see more culture-clashing fusion foods here. Asian vegetables on pizza? I could see it!
I like to consider myself well traveled throughout the state of Florida, but one city that I had never been to was Delray Beach. For some reason I always went further north or south of Delray and never actually stopped to explore rather than driving through. On a recent morning, I decided to change that and was actually surprised by Delray. The city's downtown was much larger than I was expecting, filled with shops, historic hotels, and countless restaurants. The decision was made to have breakfast at one of these restaurants called the Green Owl.
The Green Owl had a sort of a retro diner look on the inside and outdoor seating on the sidewalk out front. We choose to eat outdoors. For food, I had the One Egg Special. This breakfast came with a scrambled egg, strip of bacon, and two pancakes. Everything on the plate was tasty, although I would have preferred actual butter for my pancakes rather than the margarine that was served. Real butter is always better!
Wall Street in Downtown Orlando: It is a short block of bars and restaurants, many with the same owner, and most not worth visiting for the food based on my experience. On a recent cold night, I had dinner at one of these bars/restaurants called the Wall Street Cantina.


text:
« Taxpayer-funded "Reefer Madness" tour coming to Oregon | Main | After 37 years, my last Betsy Thelan haircut »
Oregon anti-drug summit cancelled. Oregon Marijuana Education Tour should be also.
Good news for advocates of ethical political campaigns.
Willamette Week is reporting that a planned Oregon Marijuana, Alcohol, and Other Drug Summit in Madras on October 1-2 has been cancelled. (See the blog post I wrote yesterday about the summit and associated tour.)
The sponsor of a government-funded anti-drug summit has cancelled the event after WW first reported it had been set timed to coincide with the fight over Measure 91, the marijuana legalization measure.
BestCare Treatment Services said late Thursday it was withdrawing from the summit, which was scheduled to include anti-drug activist Kevin Sabet. WW's story raised questions about the timing of a tour that would include Sabet within weeks of voters receiving their ballots for the general election.
I just left a comment on the Willamette Week story.
I hope the whole Oregon Marijuana Education Tour is cancelled also. Last night I called this the "Reefer Madness Tour" in a blog post about this underhanded attempt to get around campaign finance laws.
Oregon's drug abuse treatment community needs to realize that going ahead with the tour will forever associate them with anti-marijuana legalization fanatics like Kevin Sabet and Josh Marquis.
Sabet and Marquis should openly debate Measure 91 proponents, not hide within forums where only opponents of Measure 91 are allowed to speak -- supported by taxpayer funds, outrageously.
A KOIN piece shows how politicized the taxpayer-funded Oregon Marijuana Education Tour really is.
"Fatalities are on the rise in Washington after they legalized marijuana," said Matt Shirtcliff with the Oregon District Attorneys Association.
[Note: Googling this claim, I couldn't find any evidence for it. But traffic fatalities in Colorado, which also legalized marijuana in 2012, are at an all-time low.]
A spokesperson for the association said some members plan to join a "Marijuana Education Tour" that is put on by the same group that recently took out a full-page, anti-marijuana ad in the New York Times.
Anti-drug activist Kevin Sabet will lead the tour, which is funded by a federal grant, through Oregon a month before Election Day and talk about marijuana. The tour is not campaigning against Measure 91.
"Sure it's around election time, but it's also to educate the citizens," said Shirtcliff.
Zuckerman said he's not buying that argument.
"Calling this an education tour is preposterous," he said. "Taxpayer money should not be covertly used to influence an election."
Like I said in my comment, drug abuse professionals should be very cautious about being connected with an underhanded anti-Measure 91 effort. Their credibility will be much diminished if citizens view this "marijuana tour" as a biased attempt to mislead voters about the dangers of legalizing pot.
Posted at 07:48 PM in Current affairs, Marijuana | Permalink

redpajama_set_name: RedPajamaCommonCrawl


text:
LUSITANIA II, ubicado en Cáceres, es el segundo superordenador de la Fundación COMPUTAEX instalado en el Centro Extremeño de iNvestigación, Innovación Tecnológica y Supercomputación (CénitS) en el año 2015. Su nombre hace referencia a la provincia romana Lusitania, cuyo territorio abarcaba gran parte de la actual región de Extremadura. La puesta en marcha de LUSITANIA II supuso una importante ampliación en relación con los recursos de cómputo ofrecidos por el superordenador LUSITANIA, incrementando notablemente la potencia de cálculo del centro. Para poder hacer uso de sus horas de cálculo, los usuarios deben presentar una petición a CénitS o la Red Española de Supercomputación (RES).

Este superordenador fue financiado, tanto por fondos FEDER por el Ministerio de Economía y Competitividad (MINECO), como por la propia Fundación COMPUTAEX, que aportó el 20 % del coste total a partir de sus fondos propios. Inicialmente fue instalado en un contenedor móvil, con el objetivo de poder realizar investigaciones sobre la movilidad, monitorización y modularidad de los Centros de Procesamiento de Datos, buscando así mejorar su sostenibilidad y eficiencia. Posteriormente fue trasladado al Centro de Procesamiento de Datos de CénitS, donde se encuentra ubicado actualmente junto al superordenador LUSITANIA.

LUSITANIA II fue presentado oficialmente el 23 de mayo de 2016, en un evento que tuvo lugar en la sede social de la Fundación COMPUTAEX y que contó con la presencia de diversas personalidades del Gobierno de Extremadura, así como con expertos en Supercomputación que ofrecieron varias ponencias relacionadas con la computación de alto rendimiento.

En octubre de 2016, el proyecto "LUSITANIA II, un superordenador en un Centro de Procesamiento de Datos al aire libre", de CénitS-COMPUTAEX, fue seleccionado como finalista en dos categorías, Smart TI Infraestructure y Smart Cloud, de la cuarta edición de los enerTIC Awards, que premian proyectos tecnológicos innovadores, comprometidos con la eficiencia energética y la sostenibilidad, así como actuaciones e iniciativas que promueven el uso de las Tecnologías de la Información y la Comunicación para la mejora de la eficiencia energética.

Características técnicas

Nodo de cómputo de memoria compartida
 1 Primergy RX4770 M2 con 4 procesadores Intel Xeon E7-4830v3  con 12 cores cada uno, a 2,1GHz, con 30MB de Caché (48 cores en total), 1,5TB de memoria RAM DDR4, 4 fuentes de alimentación y discos SAS de 300GB.

Clúster de memoria distribuida
 10 chasis Fujitsu Primergy CX400 con capacidad para albergar hasta 4 servidores cada uno.
 40 servidores Fujitsu Primergy CX2550 con 2 procesadores Intel Xeon E5-2660v3, de 10 cores cada uno, a 2,6GHz (20 cores por nodo, 800 cores en total) y 25 MB de Caché, con 80GB de RAM y 2 discos SSD 128GB.

Nodos de servicio
 3 servidores Fujitsu Primergy RX2530 M1, cada uno con 2 procesadores Intel Xeon E5-2620v3 (6 cores a 2,4GHz y 15 MB de Caché); 32GB de RAM DDR4, 2 discos SAS de 300GB.

Nodos de desarrollo
 2 servidores Fujitsu Primergy RX2530 M1 con 2 procesadores Intel Xeon E5-2620v3 (6 cores a 2,4GHz y 15 MB de Caché); 64GB de RAM DDR4, 2 discos SAS de 300GB.

Almacenamiento
 Cabina de metadatos (MDT) Eternus DX 200S3 (15 discos de 900GB SAS) = 12 TB.
 2 servidores Fujitsu Primergy RX2530 M1 con 2 procesadores Intel Xeon  E5-2620v3 (6 cores a 2,4GHz y 15 MB de Caché); 64GB de RAM DDR4 y 2 discos SAS de 300GB para gestión de metadatos con Lustre.
 Cabina de datos (OST) Eternus DX 200 (41 discos de 2TB NL-SAS) = 82TB.
 2 servidores Fujitsu Primergy RX2530 M1 con 2 procesadores Intel Xeon  E5-2620v3 (6 cores a 2,4GHz y 15 MB de Caché); 64GB de RAM DDR4, 2 discos SAS de 300GB para gestión de los objetos con Lustre.

Topología de red
El superordenador está conectado con el exterior a través de una conexión de hasta 10Gbps con la Red Científico Tecnológica de Extremadura, que une las principales ciudades y centros tecnológicos de la región, interconectada a su vez con RedIRIS y con la red europea GÉANT.

Internamente, la infraestructura de servicio y cálculo se vertebra sobre:
 Un firewall Fortinet Fortigate 3810A como sistema de seguridad perimetral, con conexiones de hasta 10 Gbps, capacidad de firewall, VPN, antivirus, detección de intrusiones y gestión de ancho de banda por conexión.
 Tres switches Brocade ICX6430 de 48 puertos y un switch Brocade ICX6430 de 24 para la red de comunicación y de gestión del supercomputador.
 Tres switches InfiniBand Mellanox IS5030 de 36 puertos QDR a 40Gbps para la red de cómputo.

Proyectos y resultados de investigación

LUSITANIA y LUSITANIA II han dado soporte a más de 100 proyectos de I+D+i, enmarcados en tres grandes líneas: Ciencias de la Tierra, Ciencias de la Vida y Ciencias Informáticas y de Comunicaciones. Así, en los últimos años ha dado soporte a líneas de investigación muy heterogéneas, que aportan soluciones en ámbitos tan diversos como los siguientes: agricultura y ganadería de precisión; eficiencia energética; impacto medioambiental; predicción climática; secuenciación genética y biomedicina; virtualización de puestos de trabajo; química computacional; observatorio del sector TIC en Extremadura; monitorización y telemetría para infraestructuras inteligentes, predictibilidad de flujos de tráfico en ciudades inteligentes, simulaciones electromagnéticas, procesamiento de imágenes y animación 3D.

De este modo, multitud de investigaciones se han visto beneficiadas por la utilización de los superordenadores LUSITANIA y LUSITANIA II, habiendo publicado sus resultados en numerosas publicaciones de impacto de ámbito internacional.

Referencias

Supercomputadoras de HPE
Ciencia y tecnología de Extremadura
Informática en España


Kauai, Hawaii's garden island, offers some of the most romantic and scenic landscapes in the world. Whether it be barefoot on a white sandy beach, by a majestic cascading waterfall, or on a seaside bluff overlooking historic Hanalei Bay and famous Bali Hai. The Island of Kauai offers the most breathtaking wedding locations found anywhere in the world.
With perfect weather just about all year round, it's no wonder Poipu is called "The Sunny South Side." The southern coastline features a series of unusual reef formations and white sand beaches. The best sunsets in Poipu are in the months of October through March, however you will see beautiful sunset colors throughout the summer months as well.
Located on the East side of the island, Kapa'a means solid in Hawaiian and is centrally located just north of Lihue. The town and its beaches are nestled at the base of Nounou Mountain, also known as Sleeping Giant. It is also called the Royal Coconut Coast.
Located on the north shore, just south of Princeville, Kilauea is home of the lush Na 'Aina Kai Botanical Gardens. The gardens offer a variety of stunning locations for ceremonies and receptions. The Hardwood Forest offers a fairytale setting with its endless rows of teak and zebrawood trees that frame a couples' day perfectly. Ka'ula Lagoon with its picturesque waterfall creates a backdrop of unrivaled beauty. Na 'Aina Kai is truly one of the most breathtaking venues on the north shore. Kilauea has some of the most exclusive beaches on the north shore. Anini beach stretches out for miles and boasts views of the Kilauea lighthouse and Kalihiwai bay.
Located between the towns of Kilauea and Hanalei, Princeville has stunning bluffs and beaches offering breathtaking views of Hanalei Bay and Makana Mountain Ridge, also known as Bali Hai. There are many hidden gems that are worth the search. Hanalei Bay Resort and Pu'u Poa Beach have great sunset views and Bali Hai across the bay. The best months for sunset are April through September.
Located on the northern most part of the island, the towns of Hanalei and Ha'ena include some of the most famous and beautiful beaches in the world. Hanalei Bay is a 3 mile crescent moon of pristine white sandy beaches with cascading mountains in the backdrop. Tunnels and Ke'e beach are at the very end of the road, and we mean the very end of the road. Stunning views of the Na Pali Coast can be seen from Ke'e which boasts sunsets year-round.
*Please note that do to the substantial flooding and landslides that occurred in April, Ha'ena and Ke'e are temporarily unavailable for commercial use. It is unclear when these locations will be reopened to the public. We are sorry for the inconvenience.


Bill Kristol is a famous Politician from USA, he/she is 66 years old and still alive, born December 23, 1952.
"These soldiers deserve a better defense secretary than the one we have"
"Surely our inaction with respect to Syria is a poor precedent if we're fighting a war on terror"
"If the American people really come to a settled belief that Bush lied us into war, his presidency will be over"
"Shouldn't Democrats insist that Sen. Durbin step down as their whip, the number two man in their leadership?"
"In any case, decisions on troop levels in the American system of government are not made by any general or set of generals but by the civilian leadership of the war effort"
"All defense secretaries in wartime have, needless to say, made misjudgments"


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Thunderstorm alert for five districts till 7.45 pm
Bhubaneswar: The local India Meteorological Department (IMD) today issued thunderstorm alert for five districts in the State between 4.45 pm and 7.45 pm.
As per the latest bulletin, moderate thunderstorm and lightning is likely to occur at one or two places in Keonjhar, Jajpur, Mayurbhanj, Bhadrak and Balasore between 4:45 pm and 7:45 pm today.
"Moderate thunderstorm/lightning with light to moderate rainfall and gusty wind speed reaching 30 to 40 kmph likely to occur at one or two places over the districts of Keonjhar, Jajpur, Mayurbhanj, Bhadrak and Balasore between 4.45 pm and 7.45 pm," said the IMD bulletin.
The people in these districts have been advised to remain alert during this period.
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What to look out for when traveling to Mexico City and beyond
Posted by admin July 16, 2021 Contact
MEXICO CITY — A big chunk of the population is going to be heading to Mexico's capital city, Mexico City, on the next leg of their travels.
On Thursday, the first of four planned train services will begin with the first train, an 8:15 a.m. train to the city's train station.
It's a rare glimpse into the country's first subway line, which opened in 2011 and is currently operated by Mexico City-based Metrolink and the state-run Metro.
MEXICO City, which sits on the Pacific Ocean at the edge of the United States, is an international city, but it's not without its own problems.
On Tuesday, a small plane crashed on a runway at the city airport.
In February, a man named Luis Felipe Ortiz Jr. was killed when a jetliner struck a bus.
It was the third fatal crash in the capital in as many years.
The country's tourism sector has been plagued by safety problems, including a string of fatal crashes, including the July 2014 crash of a passenger jet near the U.S. border that killed 39 people and injured dozens more.
Mexico City is also known as "El Chapo City," which is shorthand for "El Guapo."
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When the dinosaurs died out some 65 million years ago, many perished in the exact same iconic pose: neck, spine, and tail curved backward, mouth open, limbs contracted. The reason for this characteristic dino death pose has been unclear. Conventional wisdom held that the dead dinos' pose was struck when the muscles contracted under rigor mortis or because the dinos' tendons and ligaments had dried up, suggesting that their bodies had been exposed to the sun for a long time. But if so, why hadn't the bones been scattered by scavengers?
Now the answer is coming from the corpses of some modern-day birds and mammals, which look very similar when they have died under certain specific conditions. The connection was never made before because paleontologists rarely see dead parrots. But veterinarians do. And luckily, Cynthia Marshall Faux is both—with doctorates in veterinary medicine as well as geology (with a specialty in vertebrate paleontology).
Adding to the intrigue is that opisthotonos is usually seen in warm-blooded animals like birds and mammals but not reptiles. Faux's paper on opisthotonos, published in March, rethinks dinosaurs not just as having died for reasons other than meteor impacts and volcanic eruptions but also advances the argument that these creatures may have had hot blood pumping through their veins.