Dynamics of Magnetically Trapped Particles: Foundations of by Juan G. Roederer

By Juan G. Roederer

This e-book is a brand new variation of Roederer’s vintage Dynamics of Geomagnetically Trapped Radiation, up-to-date and significantly improved. the most aim is to explain the dynamic homes of magnetically trapped debris in planetary radiation belts and plasmas and clarify the actual tactics concerned from the theoretical standpoint. The procedure is to ascertain intimately the orbital and adiabatic movement of person debris in general configurations of magnetic and electrical fields within the magnetosphere and, from there, derive uncomplicated good points of the debris’ collective “macroscopic” habit in most cases planetary environments. Emphasis isn't really at the “what yet at the “why of particle phenomena in near-earth house, supplying a fantastic and transparent knowing of the valuable easy actual mechanisms and dynamic tactics concerned. The ebook also will function an creation to normal area plasma physics, with considerable easy examples to demonstrate and clarify the actual foundation of other kinds of plasma present structures and their self-organizing personality through the magnetic box. the final word target is to aid either graduate scholars and scientists to effectively face the theoretical and experimental demanding situations mendacity forward in area physics in view of contemporary and upcoming satellite tv for pc missions and an anticipated wealth of knowledge on radiation belts and plasmas.

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Sample text

We assume only the direction of U as known, but not its modulus. Call vP and vQ the velocities along the x axis of the particle at points P and Q, respectively (consider one of these velocities as given). 6) and with v D v ? 11). 9). 19) can be expressed as a function of vP or vQ : C ˇ m ˇˇ vP D qB ˇ ˇ ˇ ˇ m ˇˇ E ˇˇ E ˇˇ D vQ C ˇ Bˇ qB ˇ B Note that this is not the radius of curvature of the trajectory in the OFR! It is interesting to compare the total forces acting in the OFR on the particle at P and Q, respectively: jfP;Q j D qvP;Q B qE D qv B 16 1 Particle Drifts and the First Adiabatic Invariant Fig.

The particle thus “reacts” perpendicularly to the external force and no average work is done on the particle during its drift motion under the present condition of a uniform field, although in the OFR, the kinetic energy of the particle changes periodically in its cyclotron turns; in the GCS, however, the perpendicular velocity is v? D const. Positive and negative particles drift in mutually opposite directions. Most importantly, V F is independent of the particles’ mass and energy. 3 Zero-Order Drifts 13 Fig.

L i' . It does not count as a zeroorder drift, however, because the phase-average force is a first-order quantity, it is not energy independent and VG v? always. We will return to this in detail in the next chapter. Let us summarize some of the principal properties of zero-order and first-order drifts, for non-relativistic, 90ı pitch angle particles. In the zero-order drift due to the action of an external force, the drift of the particle is independent of its energy; the orbit in the original frame of reference is in general a cycloid and the particle velocity is variable (periodic).

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