Presentation is loading. Please wait.

Presentation is loading. Please wait.

HIGH-FREQUENCY KINETIC INSTABILITIES DRIVEN BY ANISOTROPIC ELECTRON BEAMS 20 March 2013 Anna Kómár 1, Gergő Pokol 1, Tünde Fülöp 2 1)Department of Nuclear.

Published byNathan Hamilton Modified over 9 years ago

Similar presentations

Presentation on theme: "HIGH-FREQUENCY KINETIC INSTABILITIES DRIVEN BY ANISOTROPIC ELECTRON BEAMS 20 March 2013 Anna Kómár 1, Gergő Pokol 1, Tünde Fülöp 2 1)Department of Nuclear."— Presentation transcript:

1 HIGH-FREQUENCY KINETIC INSTABILITIES DRIVEN BY ANISOTROPIC ELECTRON BEAMS 20 March 2013 Anna Kómár 1, Gergő Pokol 1, Tünde Fülöp 2 1)Department of Nuclear Techniques, Budapest University of Technology and Economics, Association EURATOM 2)Department of Applied Physics, Chalmers University of Technology and Euratom-VR Association I. Chalmers Meeting on Runaway Electron Modelling

2  Description of the instability  Runaway electron distributions  Wave dispersions  Growth rate of the waves  Critical runaway densities  Plans, current problems Outline 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling 2/29

3 Runaway distribution 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling T. Fülöp, PoP 13(062506), 2006 p = γv e /c normalized momentum 3/29 Anisotropic → Instabilities

4 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling response Imaginary part Growth rate Particle-wave interaction Dispersion of the plasma waves: (homogeneous plasma) Dielectric tensor Perturbative analysis k : wave number ω : wave frequency c : speed of light 4/29

5 General resonance condition Ultrarelativistic resonance condition Generalizations 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling Magnetosonic- whistler wave Electron-whistler, EXEL wave High electric field distribution function Near-critical field distribution function 5/29

6 Near-critical distributionAvalanche distribution Distribution function 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling T. Fülöp, PoP 13(062506), 2006P. Sandquist, PoP 13(072108), 2006 6/29 p = γv e /c normalized momentum

7 Distribution function  Qualitatively similar  Lower electric field → less anisotropy  Growth rate of the waves:  Ensured by the anisotropy  Not affected by the details 20 March 2013 7/29 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling

8 Electron plasma waves 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling  Relaxing the electromagnetic approximation:  Approximations for the dielectric tensor: 8/29 T.H. Stix, Waves in Plasmas (AIP, 1992)

9 Electron plasma waves 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling  Dielectric tensor:  Wave dispersion: 9/29

10 Electron plasma waves 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling 10/29  Qualitatively different for B > 2.6 T

11 Electron plasma waves 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling 11/29

12 Electron plasma waves 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling 12/29  Cold plasma approximation is used (th. motion << gyro-motion)  Validity: 20 keV, 10 keV, 1 keV

13 Calculating the growth rate of the waves 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling 13/29 Unperturbed dispersion: Perturbed dispersion: The wave frequency changes: → Calculating the runaway susceptibilities:

14 General resonance condition 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling  Resonance condition: implicit UltrarelativisticGeneral case 14/29 T.H. Stix, Waves in Plasmas (AIP, 1992)

15 Restrictions on the wave dispersion 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling Resonant momentum is physical if: (1) (2) and Whistler and high-k region of EXEL 15/29 and

16 Growth rate in near-critical field (Whistler) 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling Maximum out of the EW region of validity 16/29 E/E c = 1.3 B = 2 T n e = 5 ∙ 10 19 m -3 n r = 3 ∙ 10 17 m -3 Order of resonance:

17 Growth rate in near-critical field (EXEL) 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling No growth rate for k < 1300 m -1 17/29 E/E c = 1.3 B = 2 T n e = 5 ∙ 10 19 m -3 n r = 3 ∙ 10 17 m -3 Order of resonance: k || c = ω 0

18 Growth rate in near-critical field 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling Electron-whistler waveExtraordinary electron wave Near-critical case → max. energy (2.6 MeV, p = 5) 18/29 most unstable wave E/E c = 1.3, B = 2 T, n e = 5 ∙ 10 19 m -3, n r = 3 ∙ 10 17 m -3 10 2 γ / ω ce

19 Damping rates of the wave, stability 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling  Collisional damping:  Convective damping:  The runaway beam has a finite radius, L r 19/29 M. Brambilla, PoP 2(1094), 1995 G. Pokol, PPCF 50(045003), 2008

20 Critical density (Whistler) 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling  Stability: Finding (Growth rate – Damping rates) = 0 (for the most unstable wave) Critical runaway density 20/29 T = 20 eV T = 1000 eV Unstable Stable E/E c = 1.3 n e = 5 ∙ 10 19 m -3

21 Critical density (EXEL) 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling 21/29  Orders of magnitude lower critical density  Break at B ~ 2.6 T (for high temperature) T = 20 eV T = 1000 eV E/E c = 1.3 n e = 5 ∙ 10 19 m -3

22 What is different with EXEL? 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling 22/29  Slightly higher growth rate  Orders of magnitude lower convective damping  Collisional damping smoothes this effect for low T E/E c = 1.3, n e = 5 ∙ 10 19 m -3, n r = 3 ∙ 10 17 m -3

23 What is different with EXEL? 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling 23/29 E/E c = 1.3, n e = 5 ∙ 10 19 m -3, n r = 3 ∙ 10 17 m -3 Parameters of the most unstable wave change from θ ~ 0

24 What is different with EXEL? 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling 24/29  For the parameters of the most unstable wave:

25  Wave instability in near-critical electric field  Generalization  Relaxing the electromagnetic approximation  General resonance condition  Linear stability  The most unstable wave is dependent on the maximum runaway energy  Stability threshold is significantly lower for the EXEL 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling Conclusions 25/29

26 Plans, current problems 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling 26/29  Growth rates for high electric field  Avalanche runaway distribution  No (or much higher) maximum energy  Whistler wave Electron-whistlerMagnetosonic-whistler T. Fülöp, PoP 13(062506), 2006 E/E c = 865 B = 2 T n e = 5 ∙ 10 19 m -3 n r = 3 ∙ 10 17 m -3

27  Extraordinary electron wave  Most unstable wave would be in the region of no-growth rate (if there is a maximum runaway energy) Plans, current problems 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling 27/29 Maximum runaway energy k || c = ω 0 This is not a problem!

28 Plans, current problems 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling 28/29  For k || c > ω 0 :  n ≤ 0   For k || c < ω 0 :  n > 0  

29 Plans, current problems 20 March 2013 A. Kómár - Kinetic instabilities driven by anisotropic electron beams Chalmers Meeting on Runaway Electron Modelling 29/29 k || c > ω 0 k || c < ω 0 n = 0, -1 n = 1  Maximum at k || c = ω 0 : with n ≠ 0

Download ppt "HIGH-FREQUENCY KINETIC INSTABILITIES DRIVEN BY ANISOTROPIC ELECTRON BEAMS 20 March 2013 Anna Kómár 1, Gergő Pokol 1, Tünde Fülöp 2 1)Department of Nuclear."

Similar presentations

Magnetic Turbulence in MRX (for discussions on a possible cross-cutting theme to relate turbulence, reconnection, and particle heating) PFC Planning Meeting.

Magnetic Turbulence in MRX (for discussions on a possible cross-cutting theme to relate turbulence, reconnection, and particle heating) PFC Planning Meeting.
Particle acceleration in a turbulent electric field produced by 3D reconnection Marco Onofri University of Thessaloniki.

Particle acceleration in a turbulent electric field produced by 3D reconnection Marco Onofri University of Thessaloniki.
Particle acceleration in plasma By Prof. C. S. Liu Department of Physics, University of Maryland in collaboration with V. K. Tripathi, S. H. Chen, Y. Kuramitsu,

Particle acceleration in plasma By Prof. C. S. Liu Department of Physics, University of Maryland in collaboration with V. K. Tripathi, S. H. Chen, Y. Kuramitsu,
TAE-EP Interaction in ARIES ACT-I K. Ghantous, N.N Gorelenkov PPPL ARIES Project Meeting,, 26 Sept. 2012.

TAE-EP Interaction in ARIES ACT-I K. Ghantous, N.N Gorelenkov PPPL ARIES Project Meeting,, 26 Sept
Electron Acceleration in the Van Allen Radiation Belts by Fast Magnetosonic Waves Richard B. Horne 1 R. M. Thorne 2, S. A. Glauert 1, N. P. Meredith 1.

Electron Acceleration in the Van Allen Radiation Belts by Fast Magnetosonic Waves Richard B. Horne 1 R. M. Thorne 2, S. A. Glauert 1, N. P. Meredith 1.
Ion Pickup One of the fundamental processes in space plasma physics.

Ion Pickup One of the fundamental processes in space plasma physics.
Non-Resonant Quasilinear Theory Non-Resonant Theory.

Non-Resonant Quasilinear Theory Non-Resonant Theory.
Neutron interaction with matter 1) Introduction 2) Elastic scattering of neutrons 3) Inelastic scattering of neutrons 4) Neutron capture 5) Other nuclear.

Neutron interaction with matter 1) Introduction 2) Elastic scattering of neutrons 3) Inelastic scattering of neutrons 4) Neutron capture 5) Other nuclear.
Alfvén-cyclotron wave mode structure: linear and nonlinear behavior J. A. Araneda 1, H. Astudillo 1, and E. Marsch 2 1 Departamento de Física, Universidad.

Alfvén-cyclotron wave mode structure: linear and nonlinear behavior J. A. Araneda 1, H. Astudillo 1, and E. Marsch 2 1 Departamento de Física, Universidad.
Instabilities of a relativistic electron beam in a plasma A Review Talk Antoine Bret Universidad Castilla la Mancha – Ciudad Real – Spain KINETIC MODELING.

Instabilities of a relativistic electron beam in a plasma A Review Talk Antoine Bret Universidad Castilla la Mancha – Ciudad Real – Spain KINETIC MODELING.
Dynamical Stability of the Intracluster Medium: Buoyancy Instabilities and Nanoastrophysics Matthew Kunz Alexander Schekochihin Schekochihin et al. 2005,

Dynamical Stability of the Intracluster Medium: Buoyancy Instabilities and Nanoastrophysics Matthew Kunz Alexander Schekochihin Schekochihin et al. 2005,
Alpha-driven localized cyclotron modes in nonuniform magnetic field K. R. Chen Physics Department and Plasma and Space Science Center National Cheng Kung.

Alpha-driven localized cyclotron modes in nonuniform magnetic field K. R. Chen Physics Department and Plasma and Space Science Center National Cheng Kung.
1 TOWARD PREDICTING VLF TRIGGERING MURI Workshop 3 March 2008 E. Mishin and A. Gibby Boston College ISR Stanford University STAR Lab.

1 TOWARD PREDICTING VLF TRIGGERING MURI Workshop 3 March 2008 E. Mishin and A. Gibby Boston College ISR Stanford University STAR Lab.
Weak Turbulence Theories Quasilinear Theory. Primary Objective of Early Efforts To understand the saturation of bump-on-tail instability To study the.

Weak Turbulence Theories Quasilinear Theory. Primary Objective of Early Efforts To understand the saturation of bump-on-tail instability To study the.
Collisional ionization in the beam body  Just behind the front, by continuity  →0 and the three body recombination  (T e,E) is negligible.

Collisional ionization in the beam body  Just behind the front, by continuity  →0 and the three body recombination  (T e,E) is negligible.
Introducing Some Basic Concepts 4.14.09. Linear Theories of Waves (Vanishingly) small perturbations Particle orbits are not affected by waves. Dispersion.

Introducing Some Basic Concepts Linear Theories of Waves (Vanishingly) small perturbations Particle orbits are not affected by waves. Dispersion.
Finite Temperature Effects on VLF-Induced Precipitation Praj Kulkarni, U.S. Inan and T. F. Bell MURI Review February 18, 2009.

Finite Temperature Effects on VLF-Induced Precipitation Praj Kulkarni, U.S. Inan and T. F. Bell MURI Review February 18, 2009.
Lecture 3: Laser Wake Field Acceleration (LWFA)

Lecture 3: Laser Wake Field Acceleration (LWFA)
Mode-Mode Resonance A linear-nonlinear process. Simple Beam Instability Let us consider It is well known that the equation supports reactive instability.

Mode-Mode Resonance A linear-nonlinear process. Simple Beam Instability Let us consider It is well known that the equation supports reactive instability.
Ionospheric Absorption Prepared by Forrest Foust Stanford University, Stanford, CA IHY Workshop on Advancing VLF through the Global AWESOME Network.

Ionospheric Absorption Prepared by Forrest Foust Stanford University, Stanford, CA IHY Workshop on Advancing VLF through the Global AWESOME Network.

Similar presentations

Ads by Google