2,279 research outputs found
Physical constraints on the coefficients of Fourier expansions in cylindrical coordinates
It is demonstrated that (i) the postulate of infinite differentiability in Cartesian coordinates and (ii) the physical assumption of regularity on the axis of a cylindrical coordinate system provide significant simplifying constraints on the coefficients of Fourier expansions in cylindrical coordinates. These constraints are independent of any governing equations. The simplification can provide considerable practical benefit for the analysis (especially numerical) of actual physical problems. Of equal importance, these constraints demonstrate that if A is any arbitrary physical vector, then the only finite Fourier terms of A_r and A_θ are those with m=1 symmetry. In the Appendix, it is further shown that postulate (i) may be inferred from a more primitive assumption, namely, the arbitrariness of the location of the cylindrical axis of the coordinate system
Magnetic reconnection from a multiscale instability cascade
Magnetic reconnection, the process whereby magnetic field lines break and then reconnect to form a different topology, underlies critical dynamics of magnetically confined plasmas in both nature and the laboratory. Magnetic reconnection involves localized diffusion of the magnetic field across plasma, yet observed reconnection rates are typically much higher than can be accounted for using classical electrical resistivity. It is generally proposed that the field diffusion underlying fast reconnection results instead from some combination of non-magnetohydrodynamic processes that become important on the ‘microscopic’ scale of the ion Larmor radius or the ion skin depth. A recent laboratory experiment demonstrated a transition from slow to fast magnetic reconnection when a current channel narrowed to a microscopic scale, but did not address how a macroscopic magnetohydrodynamic system accesses the microscale. Recent theoretical models and numerical simulations suggest that a macroscopic, two-dimensional magnetohydrodynamic current sheet might do this through a sequence of repetitive tearing and thinning into two-dimensional magnetized plasma structures having successively finer scales. Here we report observations demonstrating a cascade of instabilities from a distinct, macroscopic-scale magnetohydrodynamic instability to a distinct, microscopic-scale (ion skin depth) instability associated with fast magnetic reconnection. These observations resolve the full three-dimensional dynamics and give insight into the frequently impulsive nature of reconnection in space and laboratory plasmas
Dual-Species Plasmas Illustrate MHD Flows
Plasma loops created in the laboratory strongly resemble structures observed in the solar corona. For example, both solar coronal loops and experimental loops exhibit remarkably uniform axial cross sections. A magnetohydrodynamic theory that was proposed to explain this phenomenon predicts that a plasma loop whose axial magnetic field is constricted at both footpoints will experience bulk flows into the loop from both ends. To test this theory, dual-species plasma loops were formed by supplying a different neutral gas to each of the two footpoints. Optical filters were then used to separately image the motion of different sections of the plasma. Bulk flows were, in fact, observed
Energy Efficiency Analysis of the Discharge Circuit of Caltech Spheromak Experiment
The Caltech spheromak experiment uses a size A
ignitron in switching a 59-μF capacitor bank (charged up to
8 kV) across an inductive plasma load. Typical power levels in the
discharge circuit are ~200 MW for a duration of ~10 μs. This
paper describes the setup of the circuit and the measurements of
various impedances in the circuit. The combined impedance of the
size A ignitron and the cables was found to be significantly larger
than the plasma impedance. This causes the circuit to behave like
a current source with low energy transfer efficiency. This behavior
is expected to be common with other pulsed plasma experiments
of similar size that employ an ignitron switch
Large density amplification measured on jets ejected from a magnetized plasma gun
Observation of a large density amplification in the collimating plasma jet ejected from a coplanar coaxial plasma gun is reported. The jet velocity is ~30 km s^-1 and the electron density increases from ~10^20 to 10^(22–23) m^-3. In previous spheromak experiments, electron density of the order 10^(19–21) m^-3 had been measured in the flux conserver region, but no density measurement had been reported for the source gun region. The coplanar geometry of our electrodes permits direct observation of the entire plasma dynamics including the source region. Analysis of Stark broadened spectral lines shows that the electron density increases by a factor of 100 as the jet collimates, with a peak density of up to 10^(22–23) m^-3. The observed density amplification is interpreted according to an MHD theory that explains collimation of current-carrying plasma-filled magnetic flux tubes. Issues affecting interpretation of Stark broadened line profiles and the possibility of using the high-density plasma jet for tokamak fuel injection are discussed
- …