Convergence properties of methods for effective operator calculations studied in a simple many-body model: J. M. Leinaas. Institute of Physics, University of Oslo, Oslo, Norway. T. T. S. Kuo. Institute of Physics, University of Oslo, Oslo, Norway, and Department of Physics, State University of New York at Stony Brook, Stony Brook, New York 11790

• Publisher: Elsevier Science
• Year: 1976
• Tongue: English
• Weight: 75 KB
• Volume: 97
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(76)90229-3

✦ Synopsis

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.