Page 2 - First fast-ion D-alpha (FIDA) measurements and simulations on C-2U

11E526-2 Deepak K. Gupta
III. DIAGNOSTIC APPLICATION IN FRCS
For FRC plasmas, in the radial direction, magnetic field is highest close to the last closed flux surface, (Rs), also known as the FRC radius (Fig. 1). The axial field decreases gradually in- side the FRC and vanishes at the null-location (R0). Inside the null-location, the magnitude of axial magnetic-field increases in the opposite direction compared to outside the null, and peaks at the center of the FRC (Fig. 1). Oppositely directed inner and outer field lines connect at some axial distance, defining the FRC length.
The presence of polarized Hanle signal in a magneti- cally confined plasma, e.g., in FRCs and cusps, may sug- gest the presence of a zero-magnetic-field null-location. With spatially resolved measurements, e.g., imaging or multiple- chord views, radial position of the null-location and its shape along with the magnetic field profile may be obtained. A 2-D imaging of stokes vectors, as typically used in solar physics applications,4 may be deployed to have full polarization details with spatial resolution.
Line radiation from the main plasma ions or impurities ions may be used for the measurement as long as it satisfies the transition conditions for the Hanle e↵ect. In FRCs, charge states of di↵erent impurities have di↵erent radial profiles due to their dependence on electron temperature (Te) and density (ne) radial profiles. A charge state needs to be selected that is present in the low field region at/near the null-location, which is typically in a high Te and ne region.
In absence of injected high-energy neutral beams in an FRC, radiation from excited neutral (hydrogen) main ions is limited to the open field line region outside the Rs where Te is low. Typically axial magnetic field in this region is large to get a measurable Hanle e↵ect signal. Injection of neutral beams in FRC provides charge-exchanged, warm-temperature (⇠Ti) hydrogen neutrals as well as beam neutrals in the core region of high Te, where magnetic field is typically low and field null exists. Radiation from these (warm and high-energy) excited neutrals may be used to measure the Hanle e↵ect. In addition, modulated beams may also be exploited for further control and enhancement.
In the presence of high collisions, absorption and emis- sion processes become uncorrelated, which depolarize the scattered light and destroy quantum interference of the Hanle e↵ect, even in the absence of magnetic field.5 For typical FRC plasmas (with ne ⇠ 1013 cm 3;Te ⇠ 100 eV) the e i collision frequency is ⇠105 s 1, which is orders of magnitude smaller than the typical radiative rates (or Einstein coe cients),
FIG. 1. (a) A simple “rigid rotor” axial magnetic field profile for an FRC. (b) An axial view of an FRC, showing null-location, R0, and FRC radius, Rs.
Rev. Sci. Instrum. 87, 11E526 (2016) A ⇠ 108 s 1, implying that the depolarization due to collision
can be ignored.
A. Axial view with external illumination source
In this diagnostic setup an intense light source, e.g., laser, of selected wavelength can be injected radially in the FRC, crossing the radially varying axial magnetic-field, including the null-locations (Fig. 2(a)). The resonant-line scattered light is collected with an axial view. Owing to the Hanle e↵ect, linearly polarized signals only at and near the null location will be observed, providing the radial position of the field null- location (Fig. 2(c)). Measurement of degree of polarization will provide the magnetic field, as per Eq. (1). In addition, the direction of polarization will also rotate with respect to zero field polarization by an angle, ↵ = 0.5 tan 1(2H), which will provide the direction of the magnetic field.6
B. Axial view with asymmetric self-illumination
Line radiation from plasma itself may provide the aniso- tropic incident radiation for the observation of Hanle e↵ect signals, without the need of an external radiation source. For example, the underlying solar disk provides the incident radi- ation for the observation of Hanle e↵ect signals in solar prom- inences.4 In FRCs, with circular symmetry, every location, except for FRC center, receives anisotropic incident radiation from the FRC itself (Fig. 2(b)). This is true for all impurities and main ion line-radiation due to their azimuthally symmetric distribution. This asymmetric illumination may be su cient for the observation of the Hanle e↵ect without the need of an external source. Moreover, instead of only two locations on the null being observable with the use of an external source, (Sec. III A), polarization signals will peak along the whole null-location circle, with the polarization in azimuthal direc- tion (Fig. 2(b)). This provides the possibility of imaging the whole null-location circle simultaneously, and hence a direct
FIG. 2. (a) Axial view with laser as a external illumination source. (b) Axial view with asymmetric self-illumination. (c) Polarization fraction due to Hanle e↵ect at two Hanle-field sensitivities. H ⇠ 1 at Hanle-field, B H .