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The Spheromak Formation Threshold

The Spheromak plasmas are formed using a coaxial gun in our formation scheme. The gun current arcs through hydrogen gas, creating a plasma. The gun current flows through the plasma, creating a large magnetic field which accelerates the plasma. The accelerated plasma encounters the stuffing flux as it exits the open end of the gun. The stuffing flux exerts a magnetic pressure opposite to the gun field pressure, pushing the plasma back into the gun. A spheromak forms when the gun field is large enough to overcome the stuffing flux. When the stuffing flux is too large, the plasma will not escape the gun and is "stuffed" in the gun. The formation threshold refers to the point beyond which increasing gun current forms spheromaks and before which the gun remains stuffed for a given stuffing flux.

For a range of gun current and stuffing flux, we have experimentally measured the magnetic field of the spheromak at the end of a small flux conserver. Although more experiments are to follow, this preliminary data clearly show the formation threshold. The average magnetic field on two magnetic probes is plotted as a function of gun current and stuffing flux in Figure 1 below.

Figure 1. Surface plot of spheromak plasma magnetic field at end of small flux conserver as a function of gun current and stuffing flux. The slope of the formation threshold is lambda=44.8 inverse meters.

The formation threshold appears as a cliff in this surface plot. For this limited range, it appears to be linear with respect to gun current and stuffing flux. This is more clearly seen on a contour plot of the same data. The slope of the formation threshold is lambda=44.8 inverse meters.

A simple model of spheromak formation uses a pressure balance of the magnetic fields. To find the formation threshold, we can set equal the magnetic pressures of the gun current and the stuffing flux. Solving for the ratio of gun current to stuffing flux,

We get a constant ratio, defined as lambda, that scales gun current with stuffing flux. Thus, any values of gun current and stuffing flux that satisdy this ratio must lie along the formation threshold line as seen in Figure 1.

Some data that was presented during the 1996 APS conference:

  1. Formation Threshold Plot: Bpolodial, SFC
  2. Formation Threshold Plot: Bpolodial, LFC
  3. Reconnection Layer Diagram (from Petschek)
  4. Experiment 0 Design Part A: Characterization
  5. Experiment 0 Design Part B: Characterization
  6. Experiment 1 Design: Reconnection
  7. What is a spheromak?

February 16, 1996 /