banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
A biased probe analysis of potential well formation in an electron only, low beta Polywell magnetic field
Rent this article for


Image of FIG. 1.
FIG. 1.

The magnitude of the magnetic field B plotted in the x-y plane intercepting four of the six field coils. The fieldlines are superimposed over the field's magnitude plot to reveal the underlying magnetic cusp structure of the Polywell.

Image of FIG. 2.
FIG. 2.

A diagram of the experimental setup showing the key biased probe positions.

Image of FIG. 3.
FIG. 3.

A high level diagram of the biased Langmuir probe driver circuit reduced to its simplest underlying components.

Image of FIG. 4.
FIG. 4.

A sample () curve fitted with the predicted function for a drifting-maxwellian. In this experiment, the probe was placed in the centre of the coil nearest to the single filament being tested. No magnetic field was present for the test. The Polywell was biased to a voltage of 150 V drawing a current of 4.5 mA.

Image of FIG. 5.
FIG. 5.

A plot of the mean energy isotropic distribution in one quadrant of a 2D Cartesian plane. When , this plot becomes a slice through a sphere. In this plot, the function has not yet been normalised, such that integration over all yields 1. Note that this plot is a slice in a Cartesian plane, and distinctly different from the projection of in to the 2D plane at right angles to the probe, which is plotted in Fig. 6 .

Image of FIG. 6.
FIG. 6.

Convergence of Eq. (11) on the monoenergetic isotropic distribution. The case shown has . As , the result converges on , which is the analytical result for the monoenergetic isotropic case.

Image of FIG. 7.
FIG. 7.

A plot of the velocity distribution from simulated data. The commercial OOPIC code was used to simulate an electron plasma with conditions approximating our experiment. The particle data were sampled in a number of spatial locations along the coil face axis. This plot shows reasonable agreement with the predicted function shown in Fig. 6 and thus supports the theoretically proposed .

Image of FIG. 8.
FIG. 8.

The two magnetic field test cases, both measured on probe A in the centre of the device. The fitted parameters for the two data sets with their respective () characteristic models are given in Table I .

Image of FIG. 9.
FIG. 9.

Four example () datasets from the high magnetic field radial profile experiment. Each dataset has been taken at a different spatial location along the coil axis.

Image of FIG. 10.
FIG. 10.

Sample of the fitting in a strong magnetic field. Shows the deviation from the fitted () in the saturation region.

Image of FIG. 11.
FIG. 11.

The spatial profile of the plasma potential in a strong magnetic field. The () characteristic at each spatial point has been fitted with the to find the spatial profile. These data show a potential well has formed in the middle of the device.

Image of FIG. 12.
FIG. 12.

Potential well formation in the low magnetic field range. The plasma potential for probes A and B is shown over a range of relatively low peak magnetic field values. As the field increases, the potential difference between the probes eventually becomes inverted and becomes progressively larger with increasing magnetic field strength.

Image of FIG. 13.
FIG. 13.

Potential well scaling with B. For each data point in Fig. 12 with , the difference in the two probe potentials is taken to be indicative of the change in overall potential well depth. The resulting trend is approximately linear.

Image of FIG. 14.
FIG. 14.

The change in potential well formation with extraction voltage, . The variation is determined by two competing parameters, the injected electron density and average energy.

Image of FIG. 15.
FIG. 15.

Potential well scaling with the injected electron current . Here, the potential difference between the two probes in Fig. 14 is assumed to be indicative of the overall change in well depth, and plotted as a function of the injected beam current.


Generic image for table
Table I.

Fitted parameters for the two data sets shown in Figure 8 . For the case of  = 15 mT, fits to both models have been listed.


Article metrics loading...


Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A biased probe analysis of potential well formation in an electron only, low beta Polywell magnetic field