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Additional info for Fusion An Introduction (Elements)
Example text
Anpenergetic ffiffiffiffiffiffiffiffiffiffiffiffiffi ion will share its energy with other ions over a time longer by a factor of mi =me . Electrons and ions exchange energy with each other over an even longer time, a factor of mi/me greater than the electron 90 deflection time. , by external heating), the electrons will come to a new equilibrium by scattering among themselves – self-equilibrating – on a fast time scale ($10À4 sec in fusion plasmas), next the ions will self-equilibrate on a somewhat slower time scale ($10À2 sec), and finally the ions and electrons will exchange energy on the slowest time scale ($10À1 sec).
3 Slab plasma example. j17 j 2 Basic Properties 18 where n0 is the uniform, unperturbed density. From Poissons equation, this charge produces an electric field Eðx1 Þ ¼ Àrw ¼ n0 e ðx0 Àx1 Þ e0 in the negative x direction. The equation of motion for the electrons at x1, is me x€1 ¼ eEðx1 Þ ¼ e 2 n0 ðx0 Àx1 Þ e0 Introducing j x0 Àx1 , this equation becomes €j þ e2 n0 j¼0 me e0 which has the oscillatory solution jðtÞ ¼ Aeivpe t þ BeÀivpe t Thus, the electrons initially at x1, are accelerated toward x0 by the field, overshoot, with a reversal of the field, and oscillate back and forth about x0 – much as would a spring which is initially stretched, then released.
Thus, the current and the magnetic field lie in isobaric surfaces, known as flux surfaces. Note that the current and the magnetic field are not parallel, except under the special condition rp ¼ 0. 1. 1 Cylindrical plasma column. and 1 2 2 2 pðrÞ ¼ m0 jz0 ða Àr Þ 4 r