MHD modes in a global gyrokinetic particle simulations

I. Holod, Z. Lin, Y. Nishimura
University of California at Irvine, Irvine, CA 92697-4575, USA
Abstract. It is established that the global alfven modes can resonantly interact with fusion alfa-particles, which makes them
important for energy confinement studies. For this purpose, the electromagnetic version of gyrokinetic toroidal particle-in-cell
code (GTC) has been developed. In the code ions are treated kinetically, while electrons are adiabatic in the zeroth order
of an expansion based on the smallness of electron-to-ion mass ratio. Toroidal coupling of shear Alfven modes leads to the
apperance of gaps in the continuum frequency spectrum. Inside these gaps Toroidal Alfven Eigenmodes (TAE) can exist. In
the simulations, starting with random perturbations of vector potential, the shear Alfven modes die out due to the continuum
damping and the dstinctive peaks inside TAE frequency gaps are observed. Linear dispersion relation of the observed modes
is compared with analytical theory to benchmark the results.
Keywords: Gyrokinetic, particle simulations, MHD modes
PACS: 52.30.Gz, 52.35.Bj
In burning plasmas, the heating by energetic a-particles provides the main energy source for thermal ions and
electrons, thus the alfa-particle transport significantly affects the performance of fusion reactor. The characteristic
velocities of a-particles are comparable to Alfvén velocity, so the wave-particle interactions with MHD modes, such
as Toroidal Alfvén Eigenmode (TAE) and Energetic Particle Mode (EPM), are likely to occur. It is established that
resonant interaction with MHD modes is the main mechanism of alfa-particle loss.
The number of modes driven unstable by a-particles is low, i.e., 5-10, in current fusion experiments, and the
dominant saturation mechanisms in this case are wave-particle trapping and redistribution of energetic particles.
However, in a larger reactor such as ITER, the toroidal mode number increases and a total number of modes excited
with similar growth rate could exceed 100. There, the nonlinear mode-mode coupling could become important and
fully developed Alfvén turbulence is expected.
The model is based on gyrokinetic description for ions and fluid-kinetic hybrid description for electrons [1]. Adopting
d f -method, the equation for ion weight function is the following:
Running a simulation without any instability drive we expect to observe the shear Alfvén waves damped in continuum
frequency range and undamped Toroidal Alfvén Eigenmodes (TAE) inside the frequency gaps (Ref.[3], [4]). The gaps
are produced by toroidal coupling between different poloidal harmonics. The radial location of the gap produced by
coupling of (m;n) and (m+1;n) modes is determined from the relation
q(r0) = (2m+1)=2n (10)
where q(r)  rBz(r)=R0Bq (r) is the safety factor, m and n are poloidal and toroidal mode numbers respectively.
The gap is centered at the intersection frequency w2
0 =v2
. The frequency width of the gap is dw e0
where e0
 a=R0. The radial width of the gap is dr  e0LA where LA is the length scale of Alfvén frequency change.
The nonperturbative treatment of energetic particles lead to the appearance of energetic particle mode (EPM), which
does not correspond to any particular MHD normal mode and would not exist in the absence of energetic component
[5], [6].
The work was supported by U.S. DOE grants DE-FC02-04ER54796 and DE-FG02-03ER54724.
1. Z. Lin, L. Chen, Phys. Plasmas 8, 1447 (2001).
2. Y. Chen, S. Parker, Phys. Plasmas 8, 441 (2001)
3. F. Zonca, L. Chen, Phys Fluids B 5, 3668 (1993).
4. C.Z. Cheng, L. Chen, M.S. Chance, Rep. Ann. Phys. 161, 21, (1985).
5. L. Chen, Phys. Plasmas 1, 1519 (1994).
6. F. Zonca, L. Chen, Bull. Am. Phys. Soc. 39, 1701 (1994).

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