No coin nor oath required. For personal study only.
The nonlinearly coupled Vlasov-Maxwell ion-plasma field equations are solved exactly for a transversely uniform subgroup of rotational modes induced by a uniform axial magnetic field. The ion orbits in momentum space are bipolar doubly periodic eigenfunctions of ion proper time, obtained in closed form as the difference between two doubly quasi-periodic Weierstrass zeta functions. The ion orbits in position space are helical-spiral doubly quasi-periodic functions of ion proper time, expressible simply in terms of doubly quasi-periodic Weierstrass sigma functions. The complete ion distributions are flexible functions of six constants of the ion motion: waveframe ion energy, transverse gyro center, an inner Hamiltonian correlating wave-frame ion momentum with wave-frame axial position, and both first and second axial integration constants. A rotary electromagnetic plane wave propagates along the axial magnetic field with complex cisoidal dependence upon wave-frame axial position. The eigenvalue determination intricately interrelates the wave propagation vector, the wave amplitude, the axial magnetic field, the double periods, and the bipole separation.
๐ SIMILAR VOLUMES
A two-step analysis is used to develop a formal description of strong interaction effects in highly absorptive hadronic atoms. First an essentially exact description of these effects is derived by applying the theory of the decay of a prepared state to the atomic cascade. Then the exact results are