H. "Momota

T." Takahashi

National Institute for Fusion Science (NIFS-Repository)

§ 17. Enhanced Loss of Plasma Particles in a Field-Reversed Configuration Attributed to Stochastic Pitch Angle Scattering Momota H. and *Takahashi T. *:Graduate University for Advanced Studies The Collisionless stochastic pitch angle scattering 1) of a charged particle in a field-reversed configuration has been reported already. Since particles located around certain closed magnetic surface if they located deep inside the separatrix, the pitch angle scattering of plasma particles gives no enhancement of direct loss of particles. Outside the separatrix, however, certain magnetic surfaces extend toward the open space or wall of a vacuum vessel. As is well known for the case of magnetic mirror trap of plasmas, the loss property of plasma particles depends in this case on the pitch. Consequently, we will have a loss process attributed to the collisionless stochastic scattering additional to the collisional particle loss. In an axially symmetric and steady field-reversed configuration, the energy Wand the canonical angular momentum P 0 are conserved. We have another constant of motion: J defined by ( 112n) f v 1_2dr, except for the domain closed to the field-null x-point. Therefore, the distribution function of plasma particles of j species can be expressed, ~(J, W,P 8 , ¢,X). Here, we have applied the cylindrical coordinates system. The spatial coordinates rand z have been transformed to the flux function <}(r;z) and the stream function X ( r;z). The equation for the distribution function takes the form, in the zero-th order collisionless regime: Other terms disappear because time derivatives of J, W, and Pq vanish. We are interested to a time averaged distribution function. For this case, the first term on the left-hand side of this equation vanishes too. Thus the distribution function keeps constant along a line of force between field-null x-points. For a gyrating particle, the time-averaged value of Pq is qlfl. Thus, the consequent distribution function can be expressed as~( J, W, lfl). The distribution function~( J, W, lfl) can be obtained as a a2t· a2t· a a~". !· D --1 +D·--1 +-D (-'J-1 +-1 )=0 VI alf/ 2 1 aJ 2 aw w aw T solution to the next order Fokker-Planck equation: 274 Collisionless stochastic pitch angle scattering gives no change in values of lfl and W. Therefore, we apply the values of D'l' and Dw derived from particle collision. The diffusion coefficient D1 includes collisional effects as well as the collisionless stochastic change that is given by the empirical formula: The boundary condition for the differential equation is determined from the loss criteria of a particle in a magnetic mirror: J<Jc. The quantity Jc is the ratio of the kinetic energy divided by the gyro-frequency at the mirror point. The distribution functionfvanishes at J=Jc. The solution to the Fokker-Planck equation can be obtained approximately by assuming a form: 1 (w+qJrp)/ a .(¢ )-e- IT <J(J) 1 T Giving: f .(W J )= aj(lf!) -(W+q1rp)IT 1 ' ,lfl T e for w < qJ(lf/) and for W > qJ(lfl) f .(w 1 )= aj(lf!) -(W+q1rp)tT . (n J -Jc J 1 , ,lfl e sm T 2 Jrnax -Jc Coefficients a/lfl) 's are obtained, and consequently the loss flux A lo/. ~)of respective species of particles, by the charge neutrality condition and vanishing its time derivative, both of which are the function of the scalar potential ¢ at the mirror point. Consequently, the Fokker-Planck equation takes the form in terms of the particle density n: D a2n(lfJ )/ + A.(lf! )= 0 VI ;alf/2 The value .A (lfl) takes a large value near the separatrix if the ion temperature is much larger than 400e V. This means that the enhancement]of particle loss in a field-reversed configuration attributed to the collosionless stochastic scattering of pitch angle appears if ion temperature is much higher than 400e V. Detailed discussions and results will be presented in a journal. 

Enhanced Loss of Plasma Particles in a Field-Reversed Configuration Attributed to Stochastic Pitch Angle Scattering

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