22F11
Cross field Passing Electrons as an Initiator of Closed Flux Surface
in Toroidal ECR Plasmas
磁場を横切る高速通過電子群による初期磁気面形成
MAEKAWA Takashi, TANAKA Hitoshi, UCHIDA Masaki, WATANABE Fumitake, YOSHINAGATomokazu*)
前川孝、田中仁、打田正樹、渡辺文武、吉永智一*)
Kyoto University, National Defense Academy of Japan*)
京都大学エネルギー科学研究科、防衛大学校応用科学群*)
A mode that describes non-inductive initiation of closed flux surface observed in EC-heated toroidal
plasmas is presented. First an equilibrium toroidal current flows in open fields under a weak externalvertical field. The fluid theory relates the pressure profile to the current profile. The current increases as theelectron pressure increases. The current channel expands vertically along the ECR layer. When the verticalfield inboard to the current channel is reduced significantly, cross field passing orbits of electrons appear.
The CFP electrons carry an additional current that closes the filed lines. The current profile is calculated byusing the velocity distribution of CFP electrons that is obtained by using the Fokker Planck theory.

An initial closed flux surface has been foundto be produced by ECH under a weak externalvertical field BVEXT in a number of tokamaks, bothin small and large devices, including CDX, LATE,DIIID, and JT60U [1-4] etc . If this non-inductive
technique is also effective to initiate closed flux
surface in fusion grade devices, it may relax thedemand of large inductive voltage from central
solenoid for discharge initiation. Present study
attempts a modeling of this non-inductive process.
The model assumes that closed flux surface isgenerated via two steps. First, there appears apressure-driven toroidal current as the plasma is EC
heated so as to counter balance the pressure
ballooning radial force of the plasma torus. Thiscurrent is a kind of equilibrium current originatedfrom the vertical charge separation drifts ofelectrons due to the curvature and gradient-B of thetoroidal field BT.
u VTF =(m v // 2 + v ⊥ 2 2qRBφ)The vertical current density is proportional to thelocal electron pressure,jVTF =2 Pe
RBφThe ion contribution may be negligible in ECR
plasmas. A return current that flows along thehelical field lines to compensate charge separation
make a toroidal current. While this current flows
only in open fields, the vertical field inboard to thisequilibrium current channel may be enormously

reduced from the external vertical field BVEXT when
this current increases up to the limit of open to
closed field. When this reduction attains to somelevel, which depends on the product of the major
radius and the external vertical field, RBVEXT, thesecond step sets in as follows.
Usually electrons are heated perpendicularly
by ECH and the resulted energetic electrons are
pitch angle scattered in both directions, forwardlyand backwardly. In the external field of BVEXT andBT, however, they are immediately lost to thevacuum vessel before they are significantly
pitch-angle scattered. The situation drasticallychanges when the equilibrium current and its field
increases as mentioned above. In this stage someforward electrons referred to as cross field passing
electrons are confined in open fields. They carryadditional toroidal current that closes the field lines.
The distribution on the confined area in the velocity
space is numerically estimated by a simplified
Fokker Planck model including EC-diffusion, pitch
angle scattering and slowing down of energetic
electrons due to collision with bulk particles.
Various associated quantities including toroidal
current and EC-power to maintain the distribution
are also estimated.
Numerical results for two cases, one for asmall low aspect ratio torus (Fig.1) and one for aconventional large torus, will be presented.
References[1] C.B. Forest et al.: Phys. Plasmas 1 (1994) 1568.
[2] T. Yoshinaga et al.: Phys. Rev. Letters 96 (2006)
125005 and Nuclear Fusion 47 (2007) 210.
[3] M. Uchida et al.: Nuclear Fusion 51 (2011) 063031[4] G.L. Jackson et al.:Nuclear Fusion 51 (2011) 083015

Fig.1. A case in small low aspect ratio torus