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

REVIEW OF SCIENTIFIC INSTRUMENTS 87, 11E526 (2016) Hanle e ect as a magnetic diagnostic for field-reversed
configuration plasmas
Deepak K. Guptaa)
Tri Alpha Energy, Inc., P. O. Box 7010, Rancho Santa Margarita, California 92688, USA
(Presented 8 June 2016; received 4 June 2016; accepted 20 July 2016; published online 16 August 2016)
Hanle e↵ect is presented as a low magnetic-field diagnostic for field-reversed configuration (FRC) plasmas. The non-perturbative technique is capable of measuring not only magnetic-field pro- file and direction but also field-null position and its shape. Conditions and configurations for the measurement are discussed. The technique is applicable to other low magnetic-field laboratory plasmas, e.g., magnetic-cusps, where measurements of low field are desirable, and it may also be extended to measure the two-dimensional vector magnetic-field. Published by AIP Publish- ing. [http://dx.doi.org/10.1063/1.4960756]
I. INTRODUCTION
Most fusion-relevant high-temperature plasma devices, such as tokamaks and stellarators, operate at high magnetic field. In these devices, diagnostic methods, e.g., Zeeman ef- fect, Faraday rotation, and motional Stark e↵ect, are used to measure a typical magnetic-field of 1 kG. However, the recent emergence of advanced beam-driven Field-Reversed Configurations (FRCs) as fusion relevant plasmas with the C- 21 and C-2U2 devices changes the paradigm. Axial-magnetic field inside an FRC is low. It becomes zero at the null-location and reverses direction to align with the external field near the separatix. Measurement of internal magnetic field pro- file is highly desirable to further enhance and understand the advanced beam-driven FRCs. Knowledge of the axial-field null-location (where Bz = 0) itself is very important. In previ- ous FRC experiments, insertable magnetic probes were used. However, for fusion relevant plasmas, high temperatures and long lifetimes prohibit the use of perturbative (and sometimes destructive) insertable probe diagnostics. A non-perturbative method is necessary to measure the internal magnetic field and null-location in fusion relevant FRCs.
This paper presents the use of the Hanle e↵ect3 as a non- perturbative diagnostic to measure the low magnetic field in an FRC plasma, including the position and shape of the zero axial-magnetic-field null-location. Although, the Hanle e↵ect is regularly used for the measurement of low magnetic field (⇠1-300 Gauss) on the sun,4 this is the first application of the e↵ect to measure the profile, amplitude, and direction of low field (including nearly zero) in a high-temperature laboratory plasma. The technique shown here is not limited to FRCs only and is applicable to other laboratory plasma magnetic-field conditions, such as magnetic cusps, where measurements of low magnetic-field are desired.
Note: Contributed paper, published as part of the Proceedings of the 21st Topical Conference on High-Temperature Plasma Diagnostics, Madison, Wisconsin, USA, June 2016.
a)dgupta@trialphaenergy.com
II. HANLE EFFECT
The Hanle e↵ect describes the modification in linear polarization of scattered resonance-line radiation in the pres- ence of a magnetic field. Incident line radiation scattered from atom (with total angular momentum of J = 1 higher level and J = 0 lower level) will be linearly polarized in the absence of magnetic field when observed perpendicular to the incident radiation. If a magnetic field is applied parallel to the direction of observation, the scattered light will primarily depolarize.
In the classical physics description, first given by Wilhelm Hanle in 1924,3 quasi-elastically bound excited electrons in an atom oscillate following the electric field vector of the incident photon. An observer viewing perpendicular to the incident radiation will see a damped harmonic oscillator, and hence a linearly polarized light. The damping rate corresponds to the radiation rate or Einstein’s coe cient, A, of the line radiation. When a magnetic field is applied along the observer’s view, electrons start precessing in the scattering plane with Larmor frequency, !L, destroying the polarization of scattered radia- tion. The combined motion of the electrons may be represented as damped rosette patterns. The observed fractional linear polarization for this condition is described as
pL=p1 , (1) 1+4H2
where H = !L/A
From a quantum physics picture, the Hanle e↵ect is a spe-
cial case of level crossing phenomenon at zero magnetic field.3 Emitted radiation from degenerated sub-levels is coherent and interferes destructively in one-direction to give linearly polar- ized light. With the application of magnetic field, degeneracy is lifted (due to Zeeman e↵ect) with the separation of sub-levels by an amount greater than their natural width, which leads to the depolarization of scattered light.
An essential part of the Hanle e↵ect is the presence of asymmetry in the excitation condition of the atoms, namely, asymmetric illumination. The diagnostic sensitivity of the Hanle e↵ect is limited to low magnetic fields close to zero and typically much less than a few hundred Gauss.
0034-6748/2016/87(11)/11E526/3/$30.00 87, 11E526-1 Published by AIP Publishing.