Transcript No Slide Title

Chalmers University of Technology
Szczecin, 23 March 2006
Meeting with Dr. B. Green Dr. B. Green (Euratom) and
Prof. A. Gałkowski (Association Euratom-IPPLM)
Selected Collaboration Issues on
Energetic Particle Effects in Tokamaks
M. Lisak, P. Sandquist, D. Anderson
Swedish Fusion Association Euratom-VR
Chalmers University of Technology, Göteborg
Yu. Kravtsov, S. Berczyński, P. Berczyński
Szczecin University of Technology and Martitime
University of Szczecin
Chalmers University of Technology
INTRODUCTION
Why we should study fast particle effects
in fusion plasmas?
 Up to now, fusion research was in a sub-critical zone, nTtE< 8.3x1020 m-3
keVs, without burn or with small burn (Q=0.61, JET)
 Burning plasma - fundamentally new physics. New phenomena to be
studied:
Alpha particles in a burning plasma with Q>10 (fa >60%) can have an
affect on
• Stability: fishbones, TAEs
• Transport: particle loss, wall heat loading
• Heating and current drive
• Edge physics: transport barriers
• Burn dynamics: He ash, thermal stability
etc
Chalmers University of Technology
 Perhaps, ITER will be the only opportunity before DEMO to study
alphas with confidence at various Q’s.
 Hence, there is a need for integrated assessment (simulations, based
on first-principle theory) of alpha particle behavior in a burning
plasma.
ITER oriented physics R&D
e. Fast particle physics
“Most of the research issues listed above (with the exception of disruption
studies) are linked to the presence of a population of fast particles. For the
investigation of fast particle effects it is not necessary to work with the Alpha
particles generated in DT operation: simulations are possible, e.g. by using
ICRH minority heating or negative NBI.”
Chalmers University of Technology
RESEARCH TOPICS WITHIN COLLABORATION
BETWEEN CHALMERS AND THE SZCZECIN
CONSORTIUM
Investigation of nonlinear dynamics of fast ion driven modes
near the instability threshold - generalization of the
Berk&Breizman theory to multi-mode scenarios (collaboration
with B. Breizman at Texas Univ. in Austin)
Effects of supra-thermal electrons and NBI and ICRH accelerated ions on sawteeth (collaboration with S. Sharapov
at JET-EFDA)
Chalmers University of Technology
Nonlinear dynamics of fast ion driven
modes
 The determination of fast ion-driven wave instabilities in reactor relevant
regimes is a problem to be solved on the way to design and construction of
an ignition device
 Fast ions are generated by RF and NBI heating and in the fusion reactions
(3.5 MeV alpha particles)
 Free energy comes from a non-monotonic / anisotropic/ inhomogeneous
velocity distribution function of fast particles
 Resonant excitation process
c
b
D
JET
1.6x108
2.2x106
3.3x105
ITER
2.7x108
0.8x106
0.3x105
  lc  k II qRb  nD  sb  0
Chalmers University of Technology
Studies of instabilities and confinement of energetic ions on JET serve as a
framework for the implementation of innovative fast ion diagnostics in
next step burning plasma devices such as ITER.
Instability
Frequency
(kHz)
Physical mechanism
Important
parameters
Possible
effects
Alpha diven
fishbones
101 -102
Prec. res. of internal m=1
mode
Beta alpha,
prec. freq.
Expulsio
n of
trapped
alphas
Alpha –
driven
Alfvén
waves (e.g.
TAE`s)
103 -104
Passing alphas with v>vA
v/vA, alpha
drift freq.,
beta gradient
Anomal
ous
alpha
loss
Alpha-loss
cone driven
Alfvén
waves
105 -106
Velocity space instability
TF ripple,
alpha density,
cycl. freq.
Alpha
losses
Chalmers University of Technology
 Linear theory
Local WKB analysis estimates the linear growth rate and the instability threshold
   f d  0
 Quasi-linear theory
Diffusion of the fast particle velocity distribution function
anomalous ion
relaxation in velocity space, anomalous fast ion losses, outward flux of lower
energy ions.

Theory of near-threshold nonlinear regimes (Berk & Breizman theory)
Typically, macroscopic plasma parameters evolve slowly compared to the
instability growth time scale. Perturbation technique is adequate near the
instability threshold.
Chalmers University of Technology
 Single-mode case (Phys. Rev. Lett. 76 (1996) 1256; Phys. of Plasmas 4 (1997) 1559)
- The mode amplitude evolves according to
f
dA
 ( f   d ) A 
dt
2

t/2
0
d 2 
t  2
0
2
3
d 1 exp( eff
 2 (    1 )) A(t   ) A(t     1 ) A (t  2   1 )
3

eff
- Steady-state, oscillating and explosive solutions depending on  
( f   d )
- Bifurcations at single-mode saturation can be analyzed
- Formation of a long-lived coherent nonlinear structure is possible
 Multi-mode case – the theory will be developed
- Resonance overlap can indicate strong nonlinear regime
- Multi-mode scenarios with marginal stability are interesting:
Full life-cycle of EPMs, starting from instability threshold: So far, described
only the initial phase.
Fishbones: Transition from an explosive growth to a slowly growing MHD
structure (i.e. island near q=1 surface).
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
 eff
( f   d )
Chalmers University of Technology
Effects of supra-thermal electrons and NBI and
ICRH - accelerated ions on sawteeth
Sawtooth oscillations are one of the most typical form of MHD activity in a tokamak plasma.
They appear in the form of oscillations of X-ray radiation, temperature, density and current in
the central plasma region and are shaped like the teeth of a saw. The internal kink-mode is
considered to be responsible for the sawtooth oscillations.
• General aim of work: Development and experimental evaluation of theoretical
models for fast particle effects in MHD phenomena.
• In particular, effects of supra-thermal electrons and NBI and ICRH- accelerated
ions on sawteeth have to be validated against JET data.
• Participation in upcoming JET experimental campaigns C15-C17 on fast particle
experiments is planned (P. Sandquist).
• Participation in the Integrated Modelling Project 2: Non-Linear MHD and
Disruptions, where redistribution of fast ions during sawtooth activity will be
studied. Presentation on the subject was given (M. Lisak) at the Sawtooth
Workshop at JET on 16-17 February 2006.
Chalmers University of Technology
The sawtooth oscillation
The core of a tokamak is subject to relaxation oscillations when q<1
Chalmers University of Technology
Fast Electron Bremsstrahlung in Low-Density, Grassy
Sawtoothing Plasmas
Low density, ICRH-only heated
plasmas on JET show transitions
to a ’grassy’ sawtooth regime
(chaotic sawteeth).
At the time of the transition, the
electric field on axis is close to
the critical electric field for
runaway production
 supra-thermal electrons might
play a role in the transition.
(P. Sandquist, S. Sharapov, M. Lisak et
al, contribution at EPS 2005)
Chalmers University of Technology
Tomographic reconstructions of FEB emission of supra-thermal electrons
(left), fast ion FEB energies (right) and intermediate energies (middle).
Chalmers University of Technology
Research plans
 Analysis for assessing generation and evolution of the suprathermal
electron population in plasmas with grassy sawteeth has to be
performed using analytical description and numerical (MHD and
transport) codes.
General kinetic Fokker-Planck theory of relativistic electrons is being
developed.
 Description of fast ion redistribution during sawtooth oscillations has to
be developed for particles with large orbit widths (generalization of the
previous work at Chalmers).
Chalmers University of Technology
Thank you !