Zur nichtlinearen Theorie der Strahl-Plasma-Wechselwirkung. II. Das asymptotische Verhalten des Systems

The asymptotic behavior of an amplifying beam-plasma-system for great distances x from the point where the beam enters the plasma is investigated on the basis of an expansion in powers of the electric field amplitude A₁. It is shown, that a necessary condition for approaching a steady state with a constant wave amplitude is that the first 2N ?1 derivations of the distribution function f₀(u) at the point u_φ vanish if the approximation is to N-th order in A₁. Further it is demonstrated, that an approximation including the third power of A₁ involves the important physical effects as mode coupling and wave amplitude saturation, and that fifth order correction terms are unimportant, if the beam parameters are chosen so that the difference between beam and phase velocities is not to small. To illustrate this point some numerical examples are considered.     

Das kritische magnetische Verhalten von EuO

Mössbauer effect and magnetization measurements were employed in order to study the static and especially the dynamic magnetic properties of the nearly Heisenberg ferromagnet EuO near its Curie temperature,T _c=69.2 °K. The critical exponent β of the spontaneous magnetization was determined to be β=0.34±0.02. It was shown that critical slowing down of spin fluctuations takes place nearT _c with spin relaxation times between 7×10^?11 sec (T=1.01T _c) and 1.5×10^?1 sec (T=1.03T _c). The experimental values of the relaxation time were found to be in satisfactory agreement with theoretically computed ones. Just belowT _c the Mössbauer spectra exhibit relaxation effects, which are characteristic for the occurence of critical super-paramagnetism. Investigations of several samples indicated quantitatively, that critical superparamagnetism has its origin in the non ideal composition of the real crystal.     

Stoßbestimmte Relaxation des Elektronenensembles im Plasma bei zusätzlicher Aufheizung durch ein elektrisches Feld. III. Das periodische Verhalten der Elektronenkomponente im elektrischen Feld großen Modulationsgrades

Collision Dominated Relaxation of the Electron Ensemble in a Plasma with Additional Heating by an Electric Field. III. The Periodic Behaviour of the Electron Component in an Electric Field with a Large Modulation Amplitude With the aid of the non-stationary Boltzmann-equation the periodic behaviour of the isotropic part of the velocity distribution of electrons and thereby determined macroscopic quantities is calculated for periodic electric fields with large modulation amplitude. The investigations concern a weakly ionized column plasma in neon under typical low and medium pressure conditions. Based on the numerical results for typical ranges of field strength and cycle times of the electric field a qualitative physical interpretation for the periodic behaviour of the electron component is obtained. The introduction of special field-dependent adjustment times allows the formalution of conditions which characterize the case of quasi-stationary behaviour and also the case of small amplitudes of modulation in the macroscopic quantities determined by the isotropic distribution function. The periodic states between these two limiting cases can be interpreted as due to two competing processes. The first one is the energy input controlled by the electric field and the second one is the energy loss in binary collisions of the electrons with the atoms.