Effect of large amplitude Fluctuations

Abstract

When the amplitudes of instability waves grow, many other modes are induced by non-linear effects. The small scale modes die out by the large damping effect which results from the diffusion along the magnetic field B (See the second term of eq. (31)). We consider the turbulent state in which the field fluctuations become stationary and homogeneous. This state corresponds to that of the positive column in strong magnetic fields with B several times greater than the critical field B_c. In this turbulent region, the discharge electric field remains constant for increasing magnetic fields. The diffusion flows are dominantly due to the field fluctuations. Therefore, we can not neglect the third order moments in eq. (11). The third order moments are determined by fourth order moments, the fourth order moments by next higher order ones, and so on. For a calculation, we must truncate this hierarchy. Then, we apply a method similar to Millionshchikov’s to the fourth order moments, mentioned before. The validity of this method will be discussed later.