Computational Methods for Kinetic Models of Magnetically by J. Killeen, G.D. Kerbel, M.G. McCoy, A.A. Mirin

By J. Killeen, G.D. Kerbel, M.G. McCoy, A.A. Mirin

Because magnetically restrained plasmas are as a rule now not present in a country of thermodynamic equilibrium, they've been studied widely with tools of utilized kinetic idea. In closed magnetic box line confinement units equivalent to the tokamak, non-Maxwellian distortions frequently happen due to auxiliary heating and delivery. In magnetic replicate configurations even the meant regular country plasma is much from neighborhood thermodynamic equilibrium due to losses alongside open magnetic box strains. In either one of those significant fusion units, kinetic versions according to the Boltzmann equation with Fokker-Planck collision phrases were profitable in representing plasma habit. The heating of plasmas by way of vigorous impartial beams or microwaves, the construction and thermalization of a-particles in thermonuclear reactor plasmas, the examine of runaway electrons in tokamaks, and the functionality of two-energy compo­ nent fusion reactors are a few examples of strategies during which the answer of kinetic equations is acceptable and, furthermore, in most cases priceless for an figuring out of the plasma dynamics. finally, the matter is to resolve a nonlinear partial differential equation for the distribution functionality of every charged plasma species when it comes to six part area variables and time. The dimensionality of the matter will be diminished via enforcing yes symmetry stipulations. for instance, fewer spatial dimensions are wanted if both the magnetic box is taken to be uniform or the magnetic box inhomogeneity enters mostly via its version alongside the course of the field.

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18). 4) by modifying the eigenvalues, Af. 56b). Note that this formula applies only if "a" is an ion and v 2 ~ vc~ = Zaletfolltma(Rm - 1) or if "a" is an electron and v 2 ~ vc~ = letfol/tme. We extend the definition of Ra to all velocities as Ra = 1 if "a" is an ion and v 2 ::::;; vc~, and Re = 00 if v 2 ~ vc~. ~ as functions of logio Ra. The distribution function U,a is set to 0 at those points where Ai is infinite. , we set (Si-s)jfl = 0 ifj > 0 and "a" or "b" equals "e". 4) are solved on a finite-difference mesh {Vj}f=i' where Vi = 0 and V 2 ::::;; vJ/(J - 1).

4. The results it Fig. 6 and Futch et al. (1972) were calculated using only the PoUl) term. 2. One sees that Q increases by about 20%. 11), using the expansion code, yield smaller corrections. 2 and good agreement is obtained when the Pz(Jl) corrections are included in the one-dimensional model. 2 and reported in Mirin et al. (1977), were performed with the modified one-dimensional code which includes the Pz(Jl) correction. 4. 2. , 1981). An earlier two-dimensional finite-difference code was developed (Killeen and Marx, 1970) which solved the un separated Fokker-Planck equation in v and () for a single ion species, under the assumption that the electrons can be represented by a Maxwellian distribution function with loss cone removed.

The results it Fig. 6 and Futch et al. (1972) were calculated using only the PoUl) term. 2. One sees that Q increases by about 20%. 11), using the expansion code, yield smaller corrections. 2 and good agreement is obtained when the Pz(Jl) corrections are included in the one-dimensional model. 2 and reported in Mirin et al. (1977), were performed with the modified one-dimensional code which includes the Pz(Jl) correction. 4. 2. , 1981). An earlier two-dimensional finite-difference code was developed (Killeen and Marx, 1970) which solved the un separated Fokker-Planck equation in v and () for a single ion species, under the assumption that the electrons can be represented by a Maxwellian distribution function with loss cone removed.

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