Vlasov model for the impedance of a rod-pinch diode

The rod-pinch diode[l,2] is a cylindrical, pinched-beam diode being developed as a radiography source[3]. 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 S MV with an impedance of 20 to SO
Cl, a FWHM pulse width of 20 to SO ns, and an anode  radius as small as 0.25 cm[l-31. The diode is designed to  run at critical current so that electrons emitted fkom the  cathode flow axially along the anode rod and pinch radially onto the rod tip. Typically, ion emission fkom 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 he properly designed to mn at critical current requires a detailed knowledge of the  diode impedance characteristics. Initially, a laminar flow model[4] 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[2]. The model of [4] was extended to  include transverse electron pressure in order to consider the effects of nonlaminar flow[S]. 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.

LVLASOV MODEL FOR THE  ELECTRON FLOW  

The geometry used in the rod-pinch diode model is illustrated in Fig. 1. Ions are emitted along the entire  length C of the anode rod and flow radially outward while electrons are only emitted from the bottom of the cathode at radius r. and flow axially in a sheath above the anode. The radius of the anode rod is r. and the inner edge of the anode sheath is at re There are two distinct regions; the sheath (rc t r t rJ contains ion and electrons, while the region between the sheath and the anode (rJ t r 2 r,) contains only ions. At z = C, the electrons pinch onto the end of the rod (not shown). Because C >> r,, Udr >> Udz  except at the end of the rod where the pinch occurs.

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