Verication of Continuum Kinetics in NIMROD


 Brandon Ball
 1 years ago
 Views:
Transcription
1 Verication of Continuum Kinetics in NIMROD CEMM Meeting, New Orleans, LA E. Held 1 J.Y. Ji 1 S. Kruger 2 NIMROD Team 1 Department of Physics Utah State University 2 TechX Corp. October 26, 2014
2 Electron, ion and hot particle DKEs in NIMROD Hazeltine's form for the rstorder drift kinetic equation in energy, ε, and magnetic moment, µ, variables: ( ) f + t (v + vd) f + µ B + t e(v + vd) f E ε = C(f ) 1 ξ 2 2ξ Transforming to pitchangle, ξ = v /v, and normalized speed, s = v/v 0, variables yields f + t (v + vd) [ f 1 ξ 2 2ξ [ ξ 2 b B B + t s 2 [ (1 ξ 2 ) b B B t + ] lnb f ξ s lnt 2 0 f s q s 2 T (v 0 + vd) E + ξ 2 E B lnb B 2 C(f )+ ] f ξ + q s 2 T (v 0 + vd) E+(1+ξ 2 ) E B lnb B 2 ] f s = 0 where [ (1 v D = E B B 2 + T 0s 2 ) ] qb + ξ 2 2 b B + 2ξ 2 µ 0J + (1 ξ 2 )µ 0J + mv 0sξ qb 2 b B. t
3 Continuum Electron and Ion DKE verication Quantitative agreement between NIMROD and NEO for (1) high aspect ratio circular equilibrium, (2) highbeta, DIIID like equilibrium, and (3) NSTX equilibrium. Consistent bootstrap currents: NIMROD, NEO, DK4D, NCLASS and Sauter. Paper written and soon to be submitted.
4 Equations for NIMROD/NEO Benchmark Solve simplied DKEs: t f 1 + v f 1 (v lnb ) 1 ξ 2 2ξ ξ f 1 C aa C ab = vd f 0 + sv D lnv 0 s f 0 e 2ε 0 s v (E ) A φ 1 s f 0. Using g 1 = f 1 (eφ 1 /T 0 )f 0 and assuming steadystate yields (Belli and Candy, 51 PPCF 2009): v g 1 v lnb 1 ξ 2 2ξ ξ g 1 C aa C ab = vd f 0 + sv D lnv 0 s f 0 e 2ε 0 s v E A s f 0.
5 Highβ Equilibrium T on axis 7.5 KeV Z(m) ν i a/v Ti T/T 0 n/n 0 f t ν i a/v Ti R(m) R(m)
6 Bootstrap Currents and Parallel Ion Flows J B = b q b B d vv g 1b, V i B = (B/n) d vv g 1i. 2.0E E+04 <J B>(AT/m 2 ) <u B>(mT/s) 1.0E E+04 NIMROD NEO Sauter NCLASS NIMROD NEO Sauter NCLASS 0.0E R(m) 0.0E R(m)
7 Ion Distribution Functions g 1i shown near outboard midplane: R=2.16, Z=
8 Ion Distribution Functions g 1i shown near outboard midplane: R=2.16, Z= NIMROD g 1i NEO g 1i v /v v /v v /v 0 v /v 0
9 NSTX Benchmark NSTX equilibrium provided by Brendan Lyons (Phys. Plasmas 19, (2012)) Z(m) ν i (a/v Ti ) T/T 0 n/n 0 f t ν i (a/v Ti ) R(m) R(m)
10 Bootstrap Currents and Parallel Ion Flows J B = b q b B d vv g 1b, V i B = (B/n) d vv g 1i. 6.0E+04 <J B>(AT/m 2 ) 3.0E+04 <u B>(mT/s) NIMROD NEO Sauter NCLASS NIMROD NEO Sauter NCLASS DK4D 0.0E R(m) R(m)
11 Verication paper to be submitted
12 Continuum Hot Particle DKE verication Ideal kink benchmark with NIMROD (continuum and δ f PIC) and M3D (δ f PIC) done. Verication and validation of NIMROD's continuum and δ f PIC hot particle algorithms for giant sawteeth (GS) in DIIID in progress. Verication and validation of NIMROD's continuum hot particle algorithm with GYRO, GTC and TAEFL for reversed shear Alfven eigenmodes (RSAE) in DIIID in progress.
13 Agreement on Ideal Kink Benchmark Ideal kink benchmark with NIMROD (continuum andδ f PIC) and M3D (δ f PIC).
14 Sawteeth stabilized by fast ions in shot #96043 Toroidal precession of highenergy tail stabilizes small sawteeth but results in giant sawteeth (Choi et al. POP, 2007).
15 NIMROD results for GS Continuum andδ f PIC growth rates for slowingdown f 0 in the same ballpark. Thermal ions and RFdriven high energy tail in beam distribution important for stabilization.
16 Highenergy tail Implemented in NIMROD for GS Continuum linear simulations with highenergy tail matching OrbitRF calculations in progress. Good scaling to 20,000 procs but signicant compute time needed.
17 GS calculations need signicant compute time Step function in June was GS calculations with 20,000 cores. (4 hours used) * (2 for MCF) * (20,000 cores) * (0.6 for regular queue) = 100,000 MPP hours.
18 Verify hot particles in NIMROD on RSAE case From Verication and validation of linear gyrokinetic simulation of Alfven eigenmodes in the DIIID tokamak, Spong, et al., Phys. Plasmas 19, (2012) Fully selfconsistent simulation of energetic particle turbulence and transport in burning plasmas must incorporate three new physics elements: kinetic eects of thermal particles at the thermal ion gyroradius (micro scale), nonlinear interactions of many meso scale (energetic particle gyroradius) shear Alfvén waves induced by the kinetic eects at the micro scale, and mesomicro couplings of the microturbulence and shear Alfvén wave turbulence. The large dynamical ranges of spatialtemporal processes further require global simulation codes to be ecient in utilizing massively parallel computers. Therefore, the studies of energetic particle physics in the burning plasma regime require a new approach using gyrokinetic turbulence simulation. In this paper, we document progress in the verication and validation of the simulation of Alfvén eigenmodes using the advanced tokamak regime of the DIIID experiment as a reference case.
19 Beam Ions Drive RSAE's in DIIID (#142111) RSAE's driven by 4.6 MW of deuterium neutrals injected at kev. Verication uses Maxwellian fast particles although TRANSPNUBEAM predicts anisotropic distribution.
20 Hot particle Maxwellian used in benchmark E. Held, J.Y. Ji, S. Kruger, NIMROD Team Veri cation of Con
21 Growth and rotation rates change with q min TAE real frequency changes as minimum in q decreases.
22 NIMROD/GYRO Eigenmode Comparisons
23 Future Work on Fast Particle Benchmarks Write fast particle verication paper that includes ideal kink benchmark (NIMROD continuum, NIMROD δ f PIC, and M3D δ f PIC) and RSAE results (verication with GTC, GYRO and TAEFL and validation with DIIID). Collaborate with TechX and Wisconsin on Giant Sawteeth problem with continuum hot particles.
24 Theory work related to CEMM JeongYoung Ji has two papers in preparation: Electron Parallel Closures for Arbitrary Collisionality provides tted kernel functions for evaluating integral electron closures. Electron Heat Transport in a Stochastic Magnetic Field uses the electron parallel heat ow closure to estimate radial heat transport in the presence of magnetic eld line uctuations.
Modelling of plasma response to resonant magnetic perturbations and its influence on divertor strike points
1 TH/P427 Modelling of plasma response to resonant magnetic perturbations and its influence on divertor strike points P. Cahyna 1, Y.Q. Liu 2, E. Nardon 3, A. Kirk 2, M. Peterka 1, J.R. Harrison 2, A.
More informationReview of the Present Status of Rotor Aerodynamics
WIND ENERGY Wind Energ., 1, 46±69 (1998) Review Article Review of the Present Status of Rotor Aerodynamics H. Snel,* Netherlands Energy Research Foundation, Petten, The Netherlands Key words: aerodynamics;
More informationBreakdown of Local Thermodynamic Equilibrium...
II Stellar Atmospheres Copyright (2003) George W. Collins, II 15 Breakdown of Local Thermodynamic Equilibrium... Thus far we have made considerable use of the concepts of equilibrium. In the stellar interior,
More informationTwodimensional turbulence: a physicist approach
Physics Reports 362 (2002) 1 62 Twodimensional turbulence: a physicist approach PatrickTabeling Laboratoire de Physique Statistique, Ecole Normale Superieure, 24 rue Lhomond, 75231 Paris, France Received
More informationOnedimensional wave turbulence
Physics Reports 398 (4) 65 www.elsevier.com/locate/physrep Onedimensional wave turbulence Vladimir Zakharov a;b,frederic Dias c;, Andrei Pushkarev d a Landau Institute for Theoretical Physics, Moscow,
More informationNUMERICAL SOLUTION OF AN EIGENVALUE PROBLEM FOR BOUNDED PLASMA
Revista Ingenierías Universidad de Medellín NUMERICAL SOLUTION OF AN EIGENVALUE PROBLEM FOR BOUNDED PLASMA Jaime H. Hoyos* Carlos A. Rodríguez** Recibido: 0/02/200 Aceptado: 26/08/20 ABSTRACT This article
More informationCombustion control and sensors: a review
PERGAMON Progress in Energy and Combustion Science 28 (2002) 107±150 www.elsevier.com/locate/pecs Combustion control and sensors: a review Nicolas Docquier 1,SeÂbastien Candel* Laboratoire EM2C, Ecole
More informationOverview of Missile Flight Control Systems
Overview of Missile Flight Control Systems Paul B. Jackson he flight control system is a key element that allows the missile to meet its system performance requirements. The objective of the flight control
More informationMission Need Statement for the Next Generation High Performance Production Computing System Project (NERSC8)
Mission Need Statement for the Next Generation High Performance Production Computing System Project () (Nonmajor acquisition project) Office of Advanced Scientific Computing Research Office of Science
More informationOn Graphite Transformations at High Temperature and Pressure Induced by Absorption of the LHC Beam
LHC Project Note 78 / 97 January 18, 1997 zazula@mail.cern.ch On Graphite Transformations at High Temperature and Pressure Induced by Absorption of the LHC Beam Jan M. Zazula CERNSL/BT(TA) Keywords: Summary
More informationTHE PROBLEM OF finding localized energy solutions
600 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 45, NO. 3, MARCH 1997 Sparse Signal Reconstruction from Limited Data Using FOCUSS: A Reweighted Minimum Norm Algorithm Irina F. Gorodnitsky, Member, IEEE,
More informationPlume structure in highrayleighnumber convection
J. Fluid Mech. (2005), vol. 000, pp. 1 33. c 2005 Cambridge University Press doi:10.1017/s002211200500618x Printed in the United Kingdom 1 Plume structure in highrayleighnumber convection By BABURAJ
More informationSome open problems and research directions in the mathematical study of fluid dynamics.
Some open problems and research directions in the mathematical study of fluid dynamics. Peter Constantin Department of Mathematics The University of Chicago Abstract This is an essay in the literal sense:
More informationThe Turbulence Problem
Leonardo da Vinci s illustration of the swirling flow of turbulence. (The Royal Collection 2004, Her Majesty Queen Elizabeth II) The Turbulence Problem An Experimentalist s Perspective Robert Ecke Turbulent
More informationThe Kondo Effect. Vijay B. Shenoy (shenoy@physics.iisc.ernet.in) Centre for Condensed Matter Theory Indian Institute of Science
The Kondo Effect Vijay B. Shenoy (shenoy@physics.iisc.ernet.in) Centre for Condensed Matter Theory Indian Institute of Science VBS The Kondo Effect 0 Overview What is Kondo effect? Motivation Why do this?
More information32. Passage of particles through matter 1
32. Passage of particles through matter 1 32. PASSAGE OF PARTICLES THROUGH MATTER...................... 2 32.1. Notation.................... 2 32.2. Electronic energy loss by heavy particles...... 2 32.2.1.
More informationControllability and Observability of Partial Differential Equations: Some results and open problems
Controllability and Observability of Partial Differential Equations: Some results and open problems Enrique ZUAZUA Departamento de Matemáticas Universidad Autónoma 2849 Madrid. Spain. enrique.zuazua@uam.es
More informationR.J. Strasser, A. Srivastava and M. TsimilliMichael
Chapter The fluorescence 25 transient as a tool to characterize and screen photosynthetic samples 445 The fluorescence transient as a tool to characterize and screen photosynthetic samples R.J. Strasser,
More informationThe Peso Problem Hypothesis and Stock Market Returns
The Peso Problem Hypothesis and Stock Market Returns Pietro Veronesi Graduate School of Business University of Chicago 1101 E. 58th St. Chicago IL 60637 USA ph: (773) 702 6348 email: pietro.veronesi@gsb.uchicago.edu
More informationThe Capital Asset Pricing Model: Some Empirical Tests
The Capital Asset Pricing Model: Some Empirical Tests Fischer Black* Deceased Michael C. Jensen Harvard Business School MJensen@hbs.edu and Myron Scholes Stanford University  Graduate School of Business
More informationDESIGN CHALLENGES OF TECHNOLOGY SCALING
DESIGN CHALLENGES OF TECHNOLOGY SCALING IS PROCESS TECHNOLOGY MEETING THE GOALS PREDICTED BY SCALING THEORY? AN ANALYSIS OF MICROPROCESSOR PERFORMANCE, TRANSISTOR DENSITY, AND POWER TRENDS THROUGH SUCCESSIVE
More informationA Case Study in Approximate Linearization: The Acrobot Example
A Case Study in Approximate Linearization: The Acrobot Example Richard M. Murray Electronics Research Laboratory University of California Berkeley, CA 94720 John Hauser Department of EESystems University
More informationWhat would have happened to the ozone layer if chlorofluorocarbons (CFCs) had not been regulated?
Atmos. Chem. Phys., 9, 2113 2128, 2009 Author(s) 2009. This work is distributed under the Creative Commons Attribution 3.0 License. Atmospheric Chemistry and Physics What would have happened to the ozone
More informationWind Flow Models over Complex Terrain for Dispersion Calculations
Cost Action 710 Preprocessing of Meteorological Data for Dispersion Models Report of Working Group 4 Wind Flow Models over Complex Terrain for Dispersion Calculations Principal Authors: Sandro Finardi
More informationTheory of EIT in an Ideal ThreeLevel System
Chapter 3 Theory of EIT in an Ideal ThreeLevel System 3.1 ThreeLevel Systems So far the interaction of a twolevel system (or series of twolevel systems) with a near resonant, monochromatic field has
More informationNonrigid point set registration: Coherent Point Drift
Nonrigid point set registration: Coherent Point Drift Andriy Myronenko Xubo Song Miguel Á. CarreiraPerpiñán Department of Computer Science and Electrical Engineering OGI School of Science and Engineering
More informationTISSUE INHOMOGENEITY CORRECTIONS FOR MEGAVOLTAGE PHOTON BEAMS
AAPM REPORT NO. 85 TISSUE INHOMOGENEITY CORRECTIONS FOR MEGAVOLTAGE PHOTON BEAMS Report of Task Group No. 65 of the Radiation Therapy Committee of the American Association of Physicists in Medicine Members
More informationJournal of Statistical Software
JSS Journal of Statistical Software February 2010, Volume 33, Issue 5. http://www.jstatsoft.org/ Measures of Analysis of Time Series (MATS): A MATLAB Toolkit for Computation of Multiple Measures on Time
More informationNUMERICAL SIMULATION OF TORNADOLIKE VORTICES. (Spine title: Numerical Simulation of Tornadolike Vortices) (Thesis format: IntegratedArticle)
NUMERICAL SIMULATION OF TORNADOLIKE VORTICES (Spine title: Numerical Simulation of Tornadolike Vortices (Thesis format: IntegratedArticle by Diwakar Natarajan Graduate Program in Civil and Environmental
More informationHigh Energy Detection. Solutions Beyond The Visible
High Energy Detection Solutions Beyond The Visible Contents Overview 03 Overview 04 Detection Beyond The Visible 06 High Energy Detection 09 The Interfaces 10 O  Open Front 11 F  FiberOptic 12 Y  Stand
More information