Characteristics of an electrostatic instability driven by transverse–longitudinal temperature anisotropy

Simulations have previously been reported which exhibit an electrostatic instability that couples thermal energy towards isotropy in a beam with transverse temperature sufficiently greater than the longitudinal temperature. The nature of this instability is observed to be insensitive to details of the initial beam distribution as well as the focusing geometry. Simulations of a uniformly-focused axisymmetric beam with an initial K–V distribution are compared to predictions of an analytic formalism which describes the instability in terms of an infinite series of transverse Gluckstern modes which become coupled to satisfy the full system of longitudinal/transverse equations. A finite truncation of the series is then used to numerically evaluate the instability characteristics.