The Polarization Response Function and Electrostatic Modes of Focused Beams

• Published in: IEEE transactions on plasma science Vol. 14; no. 1; pp. 11 - 16
• Main Authors: Gnavi, Graciela, Gratton, Fausto T.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.1986; Institute of Electrical and Electronics Engineers
• Subjects: Electrons; Electrostatics; Exact sciences and technology; Integral equations; Particle beams; Physics; Physics of gases, plasmas and electric discharges; Physics of plasmas and electric discharges; Plasma applications; Plasma properties; Plasma stability; Plasma waves; Polarization; Stability analysis; Waves, oscillations, and instabilities in plasmas and intense beams; Particle beam; Response function; Plasma; Instability; Polarization function; Electrostatic focusing
• ISSN: 0093-3813; 1939-9375
• DOI: 10.1109/TPS.1986.4316490

It is shown that the method of percussion for obtaining the spatial-temporal representation of the polarization response function directly [1] can also be used to study stability problems in nonuniform plasmas, thus providing a physical and mathematical alternative to the traditional approach. As an example, the stability analysis of particle beams is given, focused with cylindrical symmetry through an axis. The integral equation for electrostatic modes is set up with the polarization response, and solved with a technique that provides both the characteristic values and an integral representation for the field. The instability of this model, which is the cylindrical counterpart of the plane symmetric counterstreaming configuration, is then discussed.