Page 3 - Absolute calibration of neutron detectors on the C-2U advanced beam-driven FRC

11E125-3 Deng et al.
Rev. Sci. Instrum. 87, 11E125 (2016)
gradient near the separatrix is typically a 1 ⇥ 1019 m 3 drop over merely 5 cm radius increase.
Although small, both the interferometry and polarimetry data are a↵ected by mechanical vibrations. As HSFIR is an add-on diagnostic, it shares the mechanical support structure for the Ruby laser for Thomson scattering, i.e., the CO2 box. When the Ruby laser fires, resonant mechanical vibration modes are excited with frequency of a few hundred Hz and amplitude of several microns, as measured by the HeNe branch of the two-color interferometer. Ninety-nine percent of the vibration is cancelled in the FIR polarimetry as the two laser beams propagate collinearly, leaving a residue of about 0.1 μm, or 0.1 in phase error. In the future FIR diagnostics, independent mechanical support structure will be designed to alleviate this issue.
It is worth noting that fine tuning the collinear alignment of the two FIR probe laser beams is critical to minimize the phase error as shown in Fig. 3(b). The fine alignment process is significantly improved by using the polarizer assembly shown in the Fig. 1 inset, where the actuators are remotely controlled. It is necessary to have a step size of 0.01 mm, which is di cult by manual control.
To illustrate the FIR polarimetry performance, shown in column (a) of Fig. 4 is the polarimetry phase error data and in column (b) is the Faraday rotation data measured in two similar plasma gun discharges, both have 500 kHz bandwidth. It is seen that less than 0.5 Faraday rotation angle can be resolved with good signal to noise ratio and high time resolution. To obtain the phase error data shown in Fig. 4(a), a polarizer was tentatively inserted into the laser beam path after the 1⁄4-wave plate to turn the two circularly polarized probe laser beams back into parallel linearly polarized waves, a technique as described in Ref. 6.
The polarimetry data in Fig. 4 show that it takes about 0.8 ms for the gun plasma to reach the CV mid-plane as the plasma gun is installed in the ends of the C-2U machine about 10 m away. The Faraday rotation angle decays after the plasma-gun discharge current terminates. The line integral density of these gun plasmas measured in the CV is ⇠0.15 ⇥ 1019 m 2 and the axial magnetic field is ⇠700 G. Considering the laser beam direction is 79 with respect to the axial magnetic field, the Faraday rotation contribution from the
FIG. 4. Upper row shows the time traces of plasma gun discharge current (Ipg) of two identical shots. Shown in the lower row are the phase error (a) and polarimetry data (b) measured by the HSFIR polarimeter.
axial field is about 0.06 , about a factor of 5 smaller than the data shown in Fig. 4. Therefore, it is reasonable to conjecture that the gun plasma has significant azimuthal magnetic field. This is consistent with the polarimetry measurement of plasma gun assisted C-2 FRC discharges, where the Faraday rotation angle due to toroidal magnetic field is on the order of 0.5 , peaking at the edge.6 However, the physics process leading to the azimuthal magnetic field remains unknown.
IV. VERIFICATION OF FRC FIELD REVERSAL
The FRC is named by its characteristic confinement magnetic field structure, where the magnetic field on the axis and on the edge of the plasma is reversed. In the past the verification of field reversal relied on internal magnetic probe measurements,12 which always led to fast termination of the plasma discharges. With HSFIR interferometer data, density profile measurement is significantly improved, so that the density profile data from a single plasma shot can be used for equilibrium reconstruction to verify FRC field reversal.
FRC plasmas are generally considered as a rigid rotor, and it is more so for C-2U in which the fast-ion pressure is about the same order of magnitude of the bulk plasma pressure, and the fast-ion orbits are rotating like rigid rotors in the ion diamagnetic direction. The plasma current in FRC is diamagnetic current mostly carried by ions as ion temperature is generally a factor of 4 or more of the electron temperature. To zeroth order, the plasma current density distribution J✓(r) is proportional to the measured electron density profile ne(r) and a constant unknown angular rotation frequency !:13
J✓(r) = ene(r)!r, (1)
where e is the electron charge, and ! is an e↵ective frequency which is about the ion diamagnetic frequency with small modification due to electron diamagnetic rotation.
Since the plasma radius is much smaller than the radius of the vacuum vessel, viscosity caused rotation profile e↵ect can be ignored. Near the mid-plane, magnetic curvature can be ignored and in a cylindrical coordinate system the axial magnetic field profile can be calculated from the current profile:
⌅r00
Bz (r) |z=0 = μ0 0 J✓(r )dr + const. (2)
By iteration the unknown rotation frequency ! in Eq. (1) and the integration constant in Eq. (2) can be determined from measured Bz at the vessel inner wall and total magnetic flux within the vessel wall. Shown in Fig. 5(a) is the evolution of density profile from shot 43 628, which is used for equilibrium reconstruction to obtain the Bz profile evolution as shown in Fig. 5(b). The thick contour line in Fig. 5(b) indicates the field reversal radius where Bz = 0. It is seen that field reversal lasts up to ⇠8 ms.
C-2U FRC field reversal can also be verified from the HSFIR polarimetry data. The polarimetry chord at y = 0 cm is only sensitive to Bz component as the laser beam is perpendicular to toroidal (azimuthal) field, and the radial field e↵ect is self-canceling as the laser beam crosses the plasma