1. magnetic confinement - ENEA - Fusione

1. MAGNETIC CONFINEMENT
45
1.3 Plasma Theory
[1.65] L. Chen, Phys.
Plasmas 1, 1519, (1994)
[1.66] L.J. Zheng, L. Chen,
and R. A. Santoro, Phys.
Plasmas 7, 2469, (2000)
[1.67] F. Zonca and L.
Chen, Phys. Plasmas 7,
4600, (2000)
[1.68] H.L. Berk, et al.,
Alfvén cascades in JET
discharges with nonmonotonic
q-profile,
Inter. Fusion Theory
Conference, (Santa Fe
2001), paper 1C54
where Θ m =s 2 and Ω A,m =0 for s≠0, and Θ m =S 2 Ω A,m /n for s=0.
With this formalism, e.g., the vorticity equation for EPM resonant excitation by ion
cyclotron resonance frequency (ICRF) becomes
⎡ 2 2 2
⎤
⎢ ∂ Ω − ΩAm
, 1 Λm
Θ
+
− + m⎥
⎛
⎢ 2
2 2 2 ⎥ ⎜
⎣∂κ Θm
( 1+
κr
) ( 1+
κ ⎝
r ) ⎦
r
2
2 2 ∂
qR0k||; mn , Am , - m 2
∂κ
r
( ) = Ω Θ
Here, Ω≡ω/ω A , ω A =νA/qR 0 , and Λ m describes the fast ion response. The structure
of (3) is very general. The factor Θ m reflects the typical radial width of the mode
structure, ∆r. In fact,
2 2 2
m Ω − ΩAm
,
∆r
≈
r0
Θm
2 ⎞
1+
κr
δφm⎟
=0
⎠
(4)
(5)
(6)
It is then obvious that the largest value of Θ m between s 2 and S 2 Ω A,m /n determines
the radial mode width and the actual form of the mode structure and dispersion
relation. Since (∆ r /r 0 ) 2 ∝|1/m 2 Θ m | may be estimated, the transition from small but
finite shear to zero shear occurs for s 2