Julio Herrera

Lyapunov stability analysis of magnetohydrodynamic plasma equilibria with axisymmetric toroidal flow

Lyapunov stability conditions for ideal magnetohydrodynamic (MHD) plasmas with mass flow in axisymmetric toroidal geometry are determined in the Eulerian representation. Axisymmetric equilibrium solutions of ideal MHD are associated to critical points of a nonlinearly conserved Lyapunov functional consisting of the sum of the total energy and the following flux‐weighted quantities: the circulation along field lines, the angular momentum, the toroidal flux, and the mass content within each flux tube. Conditions sufficient for Lyapunov stability of these equilibria against axisymmetric perturbations are found by taking advantage of the Hamiltonian formalism for ideal MHD. In particular [see Eq. (60)], it is sufficient for Lyapunov stability under linearized dynamics that an axisymmetric equilibrium be subsonic in the appropriate rotating frame, lie in the first elliptic regime of the Bernoulli–Grad–Shafranov (BGS) system of equations, and satisfy one additional, more complicated, condition. Effects of bound...

Reaction-diffusion equations in one dimension: particular solutions and relaxation

Abstract Reaction-diffusion equations for the concentration of one species in one spatial dimension are considered, where the diffusion coefficient, as well as creation and annihilation terms are monomials. When the exponent of the annihilation term is smaller than the one of the creation term, unstable equilibrium solutions may exist. In the opposite case, travelling wave solutions are found in phase space, yielding the value of speed, even when the wave form cannot be written in closed form. The stability of some solutions is studied numerically, showing their robustness. In the case of nonlinear diffusion it is found that localized initial conditions evolve to the stable steady state via the travelling waves. The invasion of the stable state into the unstable one is via a travelling front with the largest possible gradient. This front can be interpreted as the final result of the growth of the most unstable mode. The exact solutions allow a modulation approach to study the problem with slowly varying coefficients. It is shown that when the creation term is of compact support in space, equilibria of compact support are also obtained.

Angular distribution of fusion products and x rays emitted by a small dense plasma focus machine

Time integrated measurements of the angular distributions of fusion products and x rays in a small dense plasma focus machine are made inside the discharge chamber, using passive detectors. The machine is operated at 37kV with a stored energy of 4.8kJ and a deuterium filling pressure of 2.75torr. Distributions of protons and neutrons are measured with CR-39 Lantrack® nuclear track detectors, on 1.8×0.9cm2 chips, 500μm thick. A set of detectors was placed on a semicircular Teflon® holder, 13cm away from the plasma column, and covered with 15μm Al filters, thus eliminating tritium and helium-3 ions, but not protons and neutrons. A second set was placed on the opposite side of the holder, eliminating protons. The angular distribution of x rays is also studied within the chamber with TLD-200 dosimeters. While the neutron angular distributions can be fitted by Gaussian curves mounted on constant pedestals and the proton distributions are strongly peaked, falling rapidly after ±40°, the x-ray distributions show...

Neutron yield and pressure evolution during a dense plasma focus device shot series

Adsorption and desorption of the filling gas, by the electrodes, the insulator and chamber materials of plasma focus devices, have been suggested as probable causes for the fluctuations in their neutron yield. This work describes analysis of data, aimed at looking for evidence to support this hypothesis. Before starting each series of discharges, a vacuum around 10−6 Torr is achieved. The filling gas, pure deuterium, is maintained under static conditions. A sudden fall of the initial pressure, around 5%, is systematically observed after the first shot in each series, before creeping back at an almost constant rate, in successive shots. On the other hand, for the first shot with fresh filling gas, the neutron yield is always low and systematically increases for the second one. The pressure evolution for the following shots shows no correlation with the neutron yield fluctuations. Thus, except for the first two shots, we find no evidence to support the hypothesis that the neutron yield fluctuations are related to an adsorption–desorption process. It is also observed that a tendency exists for the last shots of each series to yield a larger number of neutrons but with a larger dispersion. This study has been done with both solid and hollow anodes, showing qualitatively similar results in both cases.

On the Zakharov equations in one dimension

In the context of Plasma Physics some equations arise which are not completely integrable, but have solitary wave solutions. The interactions between these waves differ from those of aristocratic eolitons. A short review is made of the case of Langmuir solitons, as described by the Zakharov equations in one dimension.

Characterization of neutron emission and measurement of the electronic density in a plasma focus device of 400J

Experimental results of anisotropy in the distribution of neutron flux and his mean energy in the radial direction (90°), and measurements of the electron density in a very small plasma focus device, PF-400J (880 nF, 30 kV, 120 kA, 400 J, 300 ns time to peak current, dI/dt~4 × lO11 A/s) are presented. The following diagnostics were applied in deuterium: Time of Flight (ToF) to estimate the neutron mean energy. An array of CR-39 (C12H16O7) nuclear track detectors covered with polyethylene located radially at several positions (between -90° to 90°) in order to determinate the angular distribution of the neutron emission. The measurements of the electron density were realized in hydrogen, and the plasma discharge was synchronized with a pulsed Nd-YAG laser (~6ns FWHM at 532nm) in order to obtain interferometric diagnostics. Discharges were performed with a charging voltage of 30±2 KV (~400J).

Time Integrated and Time Resolved Neutron Measurements in a Plasma Focus Device

This work reports some experimental results on neutron emission from the pinch phase of the plasma focus device PACO (2 kJ, 31 kV). An evaluation of the building structure influence on neutron yield measurements was made. Special devices supporting CR‐39 detectors were designed, constructed and used for this purpose. Scintillator‐photomultiplier systems were used to made time‐resolved neutron detection. Angular dependence of neutron pulses was observed doing simultaneous measurements at three different angular positions of the time‐resolved detectors. Time‐of‐flight neutron measurements were also done to estimate the scattering influence. This work shows that the scattering effect is not relevant in our experiment, at least for r ⩽ 2 m. So that in this limit it is not necessary do any correction by the scattering. The average forward to radial neutron yield anisotropy is found to be 1.59 ±0.12. The neutron energy anisotropy measurements by time‐of‐flight don’t offer relevant results about the neutron prod...

Neutron Emission and Angular Distribution in Compact Plasma Focus Devices Operating at Hundreds of Joules

Measurement of anisotropy and neutron energy of the very small device PF‐400J (880 nF, 30 kV, 120 kA, 400 J, 300 ns time to peak current, dI/dt∼4×1011 A/s) are presented. Neutron emission with the device operating in deuterium has been obtained and the maximum total neutron yield measured is of the order of 106 per shot at 9mbar. The following diagnostics have been applied: time of flight (TOF) to estimate the neutron mean energy, and angular distribution of the neutron emission using CR‐39 nuclear track detectors covered with polyethylene located at several positions (between −90° to 90°). Discharges were performed at different pressures, 5–12 mbar, with a charging voltage of 30±2 KV (∼400J). With the results of the TOF measurements a mean neutron energy of (2.4±0.4) MeV was obtained. The angular measurements are compared with the total neutron yield (integral of the angular measurements). The results are consistent with an angular uniform plateau (isotropic emission) plus a shape peaked in the direction...

Physics education: elitism and errors

In his debate with Jonathan Osborne (January pp27–29), Mark Ellse is right to say that physics teaching should be focused on the elite minority of pupils who want to specialize in the subject. But I would go further and ask, why should we bother exposing every schoolchild in the country to science until the age of 16 at all? Why should every child have scientific theory rammed down their throats, for 20% of each week, year after year?

Simple Diffraction Processes for Nagumo‐ and Fisher‐type Diffusion Fronts

The diffraction of a diffusion front by concave and convex wedges is studied for Nagumo and Fishers equations on the limit of fast reaction and small diffusion, using both the asymptotic theory and full numerical solutions. For the case of a convex corner, the full numerical solution confirms that the front evolves according to the asymptotic theories. On the other hand, for the concave corner, it is shown numerically that the diffraction produces at the corner a region of low values of the solution for both the Nagumo and Fishers equations. Moreover, in both cases, the front eventually evolves, leaving behind a cavity. In the case of the Nagumo equation, it is shown that the long-term behavior of the diffraction front is just a traveling front, bent at the sloping wall. The bent region maintains its size as the front travels. This behavior is predicted by an exact traveling wave solution of the asymptotic equation for the front propagation. Good agreement is found between the numerical and the asymptotic solutions. On the other hand, behavior of the diffracted front for Fishers equation is different. In this case, the front is bent at the sloping wall, but, as time passes, the bend becomes smaller and moves toward the sloping wall. This behavior is, again, predicted by the asymptotic solution. The numerics strongly suggest that the final state for the concave corner is a steady cavity-like solution with low values at the corner and high values away from it. This solution has an angular dependence that varies with the angle of the sloping wall.