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Nonexistence of looping trajectories in hydromagnetic waves of finite amplitude. Breaking of waves in a cold collision-free plasma in a magnetic field. On stabilities of periodic waves in a cold collision-free plasma in a magnetic field.

Citation

Yeh, Tyan (1968) Nonexistence of looping trajectories in hydromagnetic waves of finite amplitude. Breaking of waves in a cold collision-free plasma in a magnetic field. On stabilities of periodic waves in a cold collision-free plasma in a magnetic field. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:04022013-142811896

Abstract

This dissertation consists of three parts. In Part I, it is shown that looping trajectories cannot exist in finite amplitude stationary hydromagnetic waves propagating across a magnetic field in a quasi-neutral cold collision-free plasma. In Part II, time-dependent solutions in series expansion are presented for the magnetic piston problem, which describes waves propagating into a quasi-neutral cold collision-free plasma, ensuing from magnetic disturbances on the boundary of the plasma. The expansion is equivalent to Picard's successive approximations. It is then shown that orbit crossings of plasma particles occur on the boundary for strong disturbances and inside the plasma for weak disturbances. In Part III, the existence of periodic waves propagating at an arbitrary angle to the magnetic field in a plasma is demonstrated by Stokes expansions in amplitude. Then stability analysis is made for such periodic waves with respect to side-band frequency disturbances. It is shown that waves of slow mode are unstable whereas waves of fast mode are stable if the frequency is below the cutoff frequency. The cutoff frequency depends on the propagation angle. For longitudinal propagation the cutoff frequency is equal to one-fourth of the electron's gyrofrequency. For transverse propagation the cutoff frequency is so high that waves of all frequencies are stable.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Applied Mathematics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Saffman, Philip G. (advisor)
  • Whitham, Gerald Beresford (co-advisor)
Thesis Committee:
  • Unknown, Unknown
Defense Date:12 September 1967
Record Number:CaltechTHESIS:04022013-142811896
Persistent URL:http://resolver.caltech.edu/CaltechTHESIS:04022013-142811896
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7574
Collection:CaltechTHESIS
Deposited By: Dan Anguka
Deposited On:02 Apr 2013 21:48
Last Modified:02 Apr 2013 21:48

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