Historical research guide · 1022 · 2014
A model of hard X-rays emission from free expanding Plasma-Focus discharges
Ezequiel O. Fogliatto · José González · M. Barbaglia · Alejandro Clausse
In one minute
A plasma focus is a simple and violent machine: two coaxial electrodes in a low-pressure gas, a capacitor bank dumped across them, and a sheet of current that runs down the gun and then collapses onto the axis into a pinch hot and dense enough to radiate. Fogliatto, González, Barbaglia and Clausse add a missing piece to the standard lumped-parameter description of that machine. Alongside the soft X-rays that come from inside the pinch, a plasma focus fires a burst of hard X-rays, and the authors model where those come from: electrons that run away from the pinch along the axial electric field, strike the base of the anode, and radiate bremsstrahlung. They compute the electric field inside the pinch from a radial current-density profile, apply the Dreicer runaway condition, and compare the result with a small open-cathode device filled with deuterium. The model reproduces the measured hard X-ray intensity as the charging voltage is raised, including the sharp fall below nine kilovolts where runaway stops.
Connection
Chapter 9 is about self-organised plasma structures — how a sheet of current becomes a compact, luminous, radiating object — and this paper is a working account of one of the beams that object throws off. It also shows the current inside the pinch sitting at the boundary rather than spread across it, which is the kind of internal structure the chapter's whole argument turns on.
From the source
During the compression a plasma focus produces X-rays by two distinct mechanisms. A soft X-ray source inside the pinch is produced by line radiation, Coulomb interaction between charged particles and recombination. A hard X-ray source of bremsstrahlung photons is produced by electrons that escape from the pinch and hit the anode base material.Section 1, Introduction
The pinch is modelled as a plasma cylinder compressed by the Lorentz force and obeying the integral magnetohydrodynamic equations, with the inner structure of the plasma column represented by Von Karman approximations of the velocity and density profiles. In this version a current density that rises with radius as the radial coordinate divided by the pinch radius, raised to a shape parameter, is included; that profile is what brings about axial and radial components of the electric field inside the pinch, which are then obtained from Ohm’s law with an azimuthal magnetic field.Section 2, Model Description, equations 1 to 6
According to Dreicer theory, a fraction of the pinch electrons escape from the pinch accelerated by the axial field if the magnitude of that field is higher than a critical value set by the particle density divided by the temperature. The energy of a single runaway electron is taken to be proportional to an effective voltage — the pinch length multiplied by the amount by which the axial field exceeds the critical field — and the total bremsstrahlung energy produced at the anode base is then estimated as proportional to the square of the incident electron energy.Section 2, Model Description, equations 7 and 8
Fitting the experiment required a high exponent in the current density profile, a shape parameter of fifty, indicating that the current is concentrated at the pinch border. The authors report that this is in agreement with previous neutron production models where the current was assumed concentrated at the external boundary.Section 3, Results; Table 1
Below nine kilovolts of charging voltage very low hard X-ray intensities were observed, which is in agreement with the absence of runaway due to the Dreicer condition. Above it the computed curve follows the measured dependence of hard X-ray intensity on charging voltage for a small plasma focus without surrounding cathode, with detectors at ninety degrees to the axis and a deuterium filling pressure of 16.4 millibar.Section 3, Results; Figure 1
The authors offer the model as a design tool: it ’offers a useful tool to calculate and design of open-cathode PF devices applied to production of pulsed beams of charged particles and hard x-rays’.Section 4, Conclusions
The way in
https://doi.org/10.1088/1742-6596/511/1/012036How to cite it
Ezequiel O. Fogliatto, José González, M. Barbaglia, Alejandro Clausse (2014) A model of hard X-rays emission from free expanding Plasma-Focus discharges doi:10.1088/1742-6596/511/1/012036