Vlasov model for the impedance of a rod-pinch diode

The rod-pinch diode [(R.A. Mahaffrey et al., 1978), (G. Cooperstein et al., 2001)] is a cylindrical, pinched-beam diode being developed as a radiography source [R.J. Commisso et al., 2002]. The diode consists of a small radius anode rod extending through the hole of an annular cathode. The diode has been operated at 1 to 5 MV with an impedance of 20 to 50 /spl Omega/, a FWHM pulse width of 20 to 50 ns, and an anode radius as small as 0.25 cm [(R.A. Mahaffrey et al., 1978), (G. Cooperstein et al., 2001), (R.J. Commisso et al., 2002)]. The diode is designed to run at critical current so that electrons emitted from the cathode flow axially along the anode rod and pinch radially onto the rod tip. Typically, ion emission from the anode is required for propagation of the pinch along the rod. Without ions, the pinch would occur on the anode rod just downstream of the cathode disk. In order to assure that a given diode will be properly designed to run at critical current requires a detailed knowledge of the diode impedance characteristics. Initially, a laminar flow model [B.V. Oliver et al., 2001] was developed to describe the rod-pinch diode. Although this model provides considerable insight into diode operation, PIC simulations show that the electron flow is not laminar [G. Cooperstein et al., 2001]. The model of [B.V. Oliver et al., 2001] was extended to include transverse electron pressure in order to consider the effects of nonlaminar flow [P.F. Ottinger et al., 2002]. However, a form for the transverse pressure tensor is required to close the equation set in this model and only special forms of the pressure tensor are analytically tractable. Here, a Vlasov model for the diode electron flow is developed using an electron distribution function with properties that are well characterized and directly related to a rod-pinch diode. In this model, the pressure tensor is self-consistently derived.