Prime pagine RA2010FUS:Copia di Layout 1 - ENEA - Fusione

magnetic confinement (cont’d.)
progress report
2010
035
|φ(r)| (Arb. units) |φ(r)| (Arb. units)
1
0.8
0.6
0.4
0.2
0
0
1
0.8
0.6
0.4
0.2
a)
1
(1,3)
b)
1
(2,3)
c)
(5,3)
(6,3)
(7,3)
0.8
0.6
(8,3)
(9,3) 0.6
0.2
(10,3)
(11,3)
0
(12,3) 0.4
-0.2
ω/ω A0 ω/ω A0
0.2
0
-1
0.4 0.8
0 0.4 0.8
-1
1
1
a) b) c)
0.8
0.6
0.4
0.2
Z/a Z/a
-0.6
0.6
0.2
0
-0.2
-0.6
0 1
0
0
-1
0 0.4 0.8
0 0.4 0.8
-1
0 1
r
r
(R-R 0 )/a
Figure 1.44 – Simulation results of KBAE excitations by energetic particles for β H = 0.009. The top panel shows the case with
no kinetic thermal ions, the bottom panel shows the one with kinetic thermal (core) ions where β ic =0.0128. Column a) is the
radial mode structure, column b) is the frequency spectrum of the electrostatic component of the fluctuating em field, and
column c) is the poloidal mode structure
ion frequency gap but also discretizing the BAE–SAW continuum. In that case, the discrete KBAEs are readily
excited by the EP drive.
The extended hybrid MHD gyrokinetic model for XHMGC has been further generalized. In order to account
for the finite parallel electric field due to parallel thermal electron pressure gradient, the parallel Ohm’s law is
modified by accounting for kinetic bulk plasma responses. Meanwhile, electron pressure gradient is added into
the vorticity equation and finite parallel electric field is taken into account in the particle motion
self–consistently. The further extended model for XHMGC allows us to confirm the theoretical predictions –
based on the generalized fishbone–like dispersion relation [1.56] – that the Alfvénic fluctuation is always the
least damped among the kinetically modified shear Alfvén and sound fluctuation branches and, thus, in
general the experimentally most relevant one[1.62].
Parametric form of equilibrium particle distribution functions for implementations in HMGC
The hybrid MHD gyrokinetic code HMGC and its extended version XHMGC [1.70] are capable of loading
a parametric form of equilibrium particle distribution functions, given in the space of particle constants of
motion. In this way is possible to use a numerically effective “delta–f scheme” without introducing any
spurious effects and numerical noise caused by a prompt relaxation of the initial distribution function. The
parametric distribution function adequately represents energetic particle populations in different situations: α
particles and supra–thermal particle tails produced by either minority ion cyclotron resonance heating (ICRH)
or (negative) neutral beam injection ((N)NBI). When FOW effects are ignorable, the parametric distribution
function readily reproduces the “slowing down” (SD) for αs, the anisotropic SD for (N)NBI and the
bi–Maxwellian for ICRH minority heating. It is possible to choose parametric dependences to fit known
profiles, such as temperature or density profiles, from experimental data or other simulation results. This
distribution function has been applied to simulate the behavior of energetic particles due to ICRH minority
heating in FAST [1.71].
Design of energetic particle equilibrium distribution functions
To the purpose of implementing an equilibrium particle distribution function in more general conditions than
those described just above, a numerical method has been developed (in collaboration with the Naka Fusion
Institute, JAEA), which allows particle simulations of toroidally confined plasmas to be initialized with a
particle distribution function F eq that owns the following properties: (i) having been constructed from
unperturbed particle orbits, F eq is an exact equilibrium that properly takes into account the effect of magnetic