The compact toroid is divided into two sub - categories: field reversed configuration and spheromak. Fig 8.2 illustrates the difference between field reversed configuration and spheromak. In a field reversed configuration
[3], the poloidal magnetic field is much stronger than the toroidal magnetic field. In a spheromak [29], the poloidal magnetic field is similar in magnitude to the toroidal magnetic field. Table 8.1 summarizes various compact toroids according to s, which is the ratio of the torus minor radius to the average ion gyroradius, according to the relative magnitudes of the poloidal magnetic field Bpand the toroidal magnetic field Bt.
For the formation of a field reversed configuration, a field reversed theta pinch or a rotating magnetic field technique are used [3]. For spheromak formation, helicity injection or a coaxial plasma gun are typically used [29]. While the current device can be ideally applied to produce both a field reversed configuration and a spheromak, the formation of a field reversed configuration requires a sophisticated setup as well as a very fast field reversal, typically a few Alfven transit times (< 1 µs), making the field reversed configuration harder to achieve in the current device. Therefore, the formation of spheromak using the current coaxial plasma source is considered.
Taylor found that the minimization of the total magnetic energy with a constant magnetic helicity leads to the following criterion [148]:
∇ × ~B = λ ~B (8.1)
which is so called the force - free condition, since ∇ × ~B = µ0J and ~~ J × ~B = 0. A resistive MHD plasma
dissipates its energy, while conserving magnetic helicity, to approach the Taylor state of minimum magnetic energy. This process is called relaxation and a spheromak is a Taylor state configuration.
For spheromak generation using a coaxial plasma gun, two parameters determine the formation of a spheromak [149, 150]: λgun= µ0I Φ λgeom= k re (8.2)
where I is the current through the plasma gun, Φ is the bias magnetic flux linking the inner and outer electrodes, and reis the effective radius of the plasma gun. k is the geometrical threshold factor where the
magnetic field from the gun is the same as the bias magnetic field. k is normally greater than 2, and 3.3817 for an infinite cylinder [151]. A spheromak - like structure is formed when λgun∼ λgeom [149, 150].
Fig 8.2 shows the relation between the plasma gun current and the required magnetic field to satisfy λgun
Table 8.1: The Compact Toroid Family [3]
s >1 s <1
Bp Bt Field Reversed Configuration
Field Reversed Mirror Astron
(a) (b)
Figure 8.2: Formation of a compact toroid in two ways. (a) Field reversed configuration formed in a field reversed theta pinch device [3, 28]. Four stages are specified: preionization, field reversal, reconnection, and contraction to an equilibrium. (b) Spheromak formation using a coaxial plasma gun[29]. The forma- tion consists of three stages: elongation of the initial magnetic field, expansion into a flux conserver, and relaxation.
0 20 40 60 80 100 0.00 0.05 0.10 0.15 0.20 0.25 0.30 M a g n e t i c F i e l d ( T )
Gun Current (kA) k 2 3.83 0 1 2 3 4 5 M a g n e t i c F l u x ( m W b )
Figure 8.3: The relation between gun current and the required magnetic field to satisfy λgun = λgeom
= λgeom. Note that two different k values are considered. Based on the geometry of the device, λgeom∼ 50,
with k = 3.8317 and 80 kA of the plasma gun current, a bias magnetic field of ∼ 0.1 T (∼ 2 mWb) is required.
8.3
Experimental Setup
The main addition to the current device is a magnet set at the plasma gun chamber. The new magnet set is composed of three electromagnets; each magnet is 11.25 inches in inner diameter, 13 inches in outer diameter, and 2 inches in thickness. The number in turns of each coil is approximately 360 turns. The inductance and resistance of each magnet is 53 mH and 1.2 Ohm, respectively. The center magnetic field per current is 1.4 × 10−3 T/A at the center of the magnet according to a gauss meter measurement.
Fig 8.3 shows the magnet set installed outside of the plasma gun chamber. Three magnet coils are assembled and installed at the plasma gun chamber. the coils are separated from one another by 2 inches. The center magnetic field is reduced to 1.1 × 10−3 T/A at the center of the magnet assembly where the
current is the total current of the three magnets. The field, however, decreases by a factor of ∼ 4 at the end of the plasma gun according to COMSOL and Maxwell 2D simulations. The magnet set is extended to the end of the chamber so that the gas puff valve is located inside the coils. This setup allows little variation of the magnetic pressure in the plasma gun as the plasma is accelerated from the end of the chamber to the front.
Figure 8.4: A picture of three magnets installed at the plasma gun chamber
The same type of capacitor bank as those used for the guiding magnets are used to pulse the magnet set. Here, the capacitor bank is 2 mF and the switch is changed to S6025 SCR (350 A peak one - cycle forward surge current) due to lower holding current (< 50 mA) than the 50RIA60 SCR (200 - 400 mA). Since the inductance of the magnets is greater than that of the guiding magnets, the 50RIA60 is not latched up to 400 V. The S6025 SCR switch can be triggered with the current trigger circuit at a magnet voltage of 200 V or higher.
8.4
Results
Fig 8.5 shows the current and the magnetic field obtained with the magnet assembly with the pulse circuit. Approximately 0.11 T of maximum magnetic field at the center of the coils is achieved at 450 V of capacitor voltage.
Fig 8.6(a) shows plasma energies measured with the magnetic field at the plasma gun. The plasma gun is discharged at - 5 kV. The plasma energy remains similar with increasing magnetic fields. However, Fig 8.6(b) shows a different trend. The plasma energy decreases significantly when the voltage on the magnets is 200 V and 400 V, while 400 V gives more plasma energy than 200 V.
The results in Fig 8.6 are interesting since there is an insignificant change of plasma energy in Fig 8.6(a) while Fig 8.6(b) shows a clear reduction at 200 V, and increase in plasma energy from 200 V to 400 V. These results imply that an embedded axial magnetic field affects the plasma transport when the field is combined with the theta pinch field. While the preliminary results show a decrease in energy, the results still open up a possibility to manipulate the plasma energy with the additional field. For example, the magnetic field at
0 50 100 150 200 250 300 350 400 450 0 20 40 60 80 100 3 coils in parallel 2 mF capacitor Current (A) Linear f it C u r r e n t ( A ) Voltage (V) I (A) ~ 0.233 x V (V) B (T ) ~ 2.56 x 10 -4 V (V) 22 ms L tot ~ 25 mH 0.00 0.02 0.04 0.06 0.08 0.10 0.12 M a g n e t i c F i e l d ( T )
Figure 8.5: The current and the magnetic field of the magnets as a function of the voltage at the capacitor
the plasma gun chamber decreases dramatically at the end of the plasma gun chamber; therefore, a stronger magnetic field may be required. Additional magnets or higher voltage operation of the pulse circuit may enable the higher magnetic field experiment.
8.5
Summary
In this chapter, it is shown that
• A compact toroid has been suggested to control plasma confinement at the plasma gun chamber and to possibly enhance plasma transport to the theta pinch and the target chamber.
• Several methods to form a compact toroid have been revisited. Spheromak formation using a coaxial plasma gun and magnets is considered as the initial candidate due to its simplicity and minimization of hardware reconfiguration. Theoretically, 0.1 - 0.25 T of magnetic field is required at the plasma gun to form a compact toroid.
• Three electromagnets are added to the current plasma gun chamber. A capacitor bank with an accompanying witching circuit is manufactured. A maximum of 0.11 T magnetic field is achieved at the center of the magnets with a capacitor voltage of 450 V.
• Experiments show little change in the plasma energy at the target chamber with the magnetic field. However, the plasma energy decreases with the magnetic field when the device is operated with the
0 100 200 300 400 0.00 0.01 0.02 0.03 0.04 0.05 Energy P l a s m a E n e r g y ( M J / m 2 ) CT Magnet Voltage (V) (a) 0 5 10 15 20 25 30 35 40 45 50 55 0.00 0.01 0.02 0.03 0.04 0.05 CT Voltage 0 V 200 V 400 V P l a s m a E n e r g y ( M J / m 2 ) Delay Time ( s) (b)
Figure 8.6: (a) Plasma energies measured with magnetic field at the plasma gun. The voltages at the magnets are 0, 200, and 400 V (b) Plasma energies measured with magnetic field at the plasma gun, theta pinch, guiding magnets, and crowbar. The voltages at the magnets are 0, 200, and 400 V
theta pinch. This suggests that the embedded magnetic field in the plasma can change the plasma transport when interacting with the magnetic field from the theta pinch.