D.5 Strapping eld assembly
D.5.2 Strapping coils
The primary role of the strapping coils is to create the strapping eld, which can repro- duce the slow-rise to fast-acceleration of laboratory plasmas. Initially, the strapping
(b)G1WeldingGcables1Gcoils
RearGinterfaceGofG dualGloopGquadGgun
(a)GEncoreGcoils (c)GCustomGcoils
SingleGloop plasmaGgun
CoaxialGconfiguration BipoleGconfiguration
ConfigurableGasGeitherGbipoleGandGcoaxial StrappingGbank
G-10 Plate G-10
Plate
VacuumG chamber port
Figure D.10: Overview of dierent coil congurations. (a) and (b) are outside the vacuum chamber, behind the plasma gun. (c) is inside the vacuum chamber in front of the plasma gun.
coils were large commercial coils placed outside of the vacuum chamber. These En- core coils were original used to generate steady-state magnetic eld for the Encore tokamak experiment [132]. The coils are sandwiched between two G-10 plates (Fig.
D.10 (a)) and mounted on adjustable stands. The stands are adjustable to mm preci- sion along thexand z axes and to cm precision along they axis. The stands can also be rotated so that the coils can be in co-axial conguration, bipole conguration, or some in-between conguration.
While this approach is optimized for exibility in strapping coils placement, it was not successful for the following reasons:
1. magnetic forces threatened to knock over the support structure if too much current were pulsed through the coils;
2. the coils were far from the plasma due to spacing limitations;
3. the large coils produce elds which did not decay sharply over the length scale of the plasma.
The rst problem limits the amount of current that could be pulsed through the Encore coils, resulting in weaker strapping eld. This weaker strapping eld was unable to signicantly inuence plasma dynamics, since the coils are located outside the vacuum chamber, far from the electrode.
One method of strengthening the coil support is to wind welding cables around the port of the vacuum chamber. This approach xes the location of the strapping
Strapping Coil
Electrodes Plasma
Figure D.11: Welding cable coils are large and placed a distance h0 behind the plane of the electrodes.
coils but allows much more current to ow through the coils. Welding cable coils are rst made from six turns of thick (4/0) welding cables around the chamber port.
These coils permit high current, but cable straps between the strapping bank and the coils fail when 26 kA is pulsed into the coils; these straps keep the cables from whipping about due to magnetic forces. The strong magnetic forces broke the straps and ejected an unknown projectile at high speeds3.
Smaller (1/0) orange welding cables replaced the (4/0) welding cables. These smaller coils (Fig. D.10 (b)) could be wrapped 13 times around the port. Since inductance scales as the number of turns squared, the quadrupled inductance leads to manageable current ow while still providing strong enough magnetic elds to inuence the plasma.
Unfortunately, there is a fundamental limitations to using large coils placed outside the vacuum chamber. Large coils produced strapping elds with large decay length.
The decay index of an axisymmetric eld is given by
n=−R B
dB
dR (D.3)
where R is the distance from an axis. Even though the bipole conguration is not axisymmetric, Eq. D.3 can be calculated along the z-axis of Fig. D.11. The coils are some distance h0 behind the electrodes and we deneh=R−h0 to be the height of
3This projectile is observed ying away from the strapping bank, but its trajectory was obscured at later times. Even though visual conrmation was obstructed, a sound was heard when the projectile collided with an unknown object. This projectile has not been found.
Hoop force
Pinch force
(a) Coil (b) (c)
Clamped here
Boron Nitride Layer
Figure D.12: (a) Magnetic forces on coil when pulsed with current. (b) Coil mounted on Delrin support structure. (c) Photo of coil.
the plasma from the electrodes. The plasma experiences a eective decay index given by
nef f =−h B
dB dh = h
Rn. (D.4)
Equation D.4 shows that large coils placed outside the vacuum chamber produce elds that look uniform from the perspective of the plasma.
Smaller coils inside the vacuum chamber are necessary to produce strapping elds which have sharp gradients and are strong enough to inuence the plasma. There is no convective cooling inside the vacuum chamber so heating is a potential issue. In order to accommodate water or air cooling, 1/4 in copper tubing was chosen as the base-material for the coil. A custom mounting structure is required because currents pulsed through the coil introduce powerful magnetic forces. The hoop force pushes the coil outwards while the pinch force squishes the coil (Fig. D.12 (a)). A professionally machined Delrin form factor is used to wind the coils and clamps placed at the coil ends hold everything together. The coils will be near the plasma so an insulating Boron Nitride layer was added to help prevent electric arcing to the coils.
The current generated by the strapping set-up is on the order of kAs and low tens of kAs depending on the coil used. The custom-coil currents at dierent strapping bank voltages are measured by a Rogowski coil. The linear t corresponds to
Icoil= 80×Vstrap−136
Hall sensor measurements at dierent strapping bank voltages show that
Bx,peak = 125 G 15V Vstrap
where Bx,peak is the peak Bx eld along the chamber axis.