We have developed explicit quantum-mechanical expressions for the conductivity and resistivity tensors of a Lorentz plasma in a magnetic field. The expressions are based on a solution to the Boltzmann equation that is exact when the electric field is weak, the electron-Fermi-degeneracy parameter Theta>>1, and the electron-ion Coulomb-coupling parameter Gamma/Z<<1. (Gamma is the ion-ion coupling parameter and Z is the ion charge state.) Assuming a screened 1/r electron-ion scattering potential, we calculate the Coulomb logarithm in the second Born approximation. The ratio of the term obtained in the second approximation to that obtained in the first is used to define the parameter regime over which the calculation is valid. We find that the accuracy of the approximation is determined by Gamma/Z and not simply the temperature, and that a quantum-mechanical description can be required at temperatures orders of magnitude less than assumed by Spitzer [Physics of Fully Ionized Gases (Wiley, New York, 1962)]. When the magnetic field B=0, the conductivity is identical to the Spitzer result except the Coulomb logarithm ln Lambda(1)=(ln chi(1)-1 / 2)+[(2Ze(2)/lambdam(e)v(2)(e1))(ln chi(1)-ln 2(4/3))], where chi(1) identical with 2m(e)v(e1)lambda/ variant Planck's over 2pi, m(e) is the electron mass, v(e1) identical with (7k(B)T/m(e))(1/2), k(B) is the Boltzmann constant, T is the temperature, lambda is the screening length, variant Planck's over 2pi is Planck's constant divided by 2pi, and e is the absolute value of the electron charge. When the plasma Debye length lambda(D) is greater than the ion-sphere radius a, we assume lambda=lambda(D); otherwise we set lambda=a. The B=0 conductivity is consistent with measurements when Z greater, similar 1, Theta greater, similar 2, and Gamma/Z less, similar 1, and in this parameter regime appears to be more accurate than previous analytic models. The minimum value of ln Lambda(1) when Z> or =1, Theta> or =2, and Gamma/Z< or =1 is 1.9. The expression obtained for the resistivity tensor (B not equal 0) predicts that eta( perpendicular )/eta( parallel ) (where eta( perpendicular ) and eta( parallel ) are the resistivities perpendicular and parallel to the magnetic field) can be as much as 40% less than previous analytic calculations. The results are applied to an idealized 17-MA z pinch at stagnation.

Particle beam diagnostic tools involving an ion beam Faraday cup, an electron beam Faraday cup, an electron magnetic spectrometer and solid-state nuclear track detectors have been used to measure the parameters of the particle beams generated by a Mather-type dense plasma focus. At a capacitor bank energy of 12.5 kJ, the energy spectra of the electron and ion beams are found to obey the same power laws: dN/dE«E~x where x = 3.5i0.5. Primary electron beam current and energy spectra were measured as a function of main bank current at pinch time, IMB-The primary electron beam current was found to scale as IMB* > reaching a magnitude of 17 kA for a device energy of 12.5 kJ. The exponent x of the electron energy spectra was found to scale as x « I ^15±0 ' 2 . These results are incorporated into an axial beam target model for neutron production, and it is found that this model could account for the magnitude and scaling of the observed neutron yield with IMB-ELECTRON BEAM ROGOWSKI COIL 4.45 CM ID ALUMINIUM DRIFT TUBE DPF HOLLOW-CENTRE ELECTRODE MAIN BANK ROGOWSKI COIL 2 TO 5 TORR ALUMINIUM BEAM DUMP ARMCO FRINGE FIELD SHIELD 50 n FARADAY CUP COLLECTOR FIG.4. Schematic view of electron magnetic spectrometer.

The design and performance of a Faraday cup which is used in a time-of-flight technique to measure the energy spectrum of ions accelerated away from the anode of a plasma focus are described. The cup is located in a differentially pumped (&lt;20 μ) chamber which is separated from the main plasma focus chamber by a 0.0457-cm diam hole positioned 16 cm above the anode. This arrangement allows a bias voltage of −400 V to be applied to the cup to stop comoving electrons and permits the observation of deuteron energies down to ∼25 keV.