Page 3 - Measuring dynamic fast ion spatial profiles with fusion protons in the Madison Symmetric Torus

10I104-3
Magee et al.
Rev. Sci. Instrum. 89, 10I104 (2018)
FIG. 3.
mator shows single pulses (red diamonds) and double pulses (blue diamonds). (Bottom frame) A zoomed-in view with ideal pulses overlaid.
and 4541 or 95% were accepted (shown with red diamonds). Peak detection found 284 pulses within the range of double hits, and of those, 276 or 97% survived to be counted (blue diamonds).
Note that the probability of a single hit registering at a given time point is P=τf =3.3×10-3, where τ = 16.67 ns is the digitization time and the rate at which pulses arrive is f ≈ 200 kHz. In the 1.2 × 106 data points recorded during the 20 ms beam-on time, we expect (and obtain) about 4000 sin- gle hits. The probability of a double hit is the square of the probability of a single hit times the number of time points of the FWHM of the pulse. From this, we estimate the num- ber of double hits to be about 230, again consistent with the measurement. We are therefore confident that the higher ampli- tude pulses are truly double hits and not x-rays or some other particles.
IV. PROFILE MEASUREMENTS A. Orbit tracing
In order to infer the fast ion density profile from the measured fusion emission profile, we must first accurately reconstruct the equilibrium magnetic field so that the 3 MeV proton orbits can be found.
At MST, the magnetic field is reconstructed from all avail- able experimental data using a non-linear Grad-Shafranov solver.12 The number of fitting free parameters is based on the number and type of available data, and fields are computed on a fine-mesh grid with ∼1.5 cm spatial resolution. The close- fitting conducting shell carries large image currents to produce the equilibrium vertical field and acts as a flux conserver. The code imposes a perfectly conducting shell boundary condition and up-down symmetry. With the shell image currents bal- ancing the plasma current, the magnetic field falls off rapidly beyond the shell inner surface.
The proton orbits are mapped in reverse in three dimen- sions to determine the possible loci of the fusion event within the plasma. Outside the machine, a straight line is drawn from the detector position through the collimator to the port- hole. The particle’s initial position and velocity upon enter- ing the region of finite magnetic field are used as initial
FIG. 4. Proton orbits or, equivalently, detector lines of sight through the plasma (colored lines) found via orbit tracing are plotted over a Shafranov- shifted, Gaussian fast ion density profile with σ = 9 cm (left). The expected fusion proton signal neglecting (blue lines) and accounting for magnetic deflection (red lines) shows that accurate orbit tracing is critical, even when ρL > a (right). The dashed lines represent ±2 cm bounds on the fast ion density profile.
conditions. The Lorentz acceleration is computed based on the instantaneous velocity and local magnetic field, neglect- ing any possible Er (which is small for the energetic proton orbit). The orbit is projected onto the R, Z plane in accor- dance with the assumption of the toroidal symmetry of the equilibrium.
Figure 4 shows, for each of the 11 experimentally real- ized collimator aiming angles, the path along which protons in the plasma will reach the detector (colored lines). The con- tour plot is a Shafranov-shifted, Gaussian density profile with σ = 9 cm (the Shafranov shift from the equilibrium recon- struction is 5 cm). The corresponding line-integrated signal is calculated and plotted on the right, in red. The dashed-dotted lines represent ±2 cm bounds on the width of the Gaussian density profile. It can be seen from the range spanned by the dashed-dotted lines that the signal is sensitive to the profile changes of this order. Also plotted in the right frame (in blue) are the expected signals from straight-line trajectories. This is a common approximation when ρL, the Larmor radius of the particle, is much larger than the minor radius of the machine, a.Here,althoughwehave ρL ≈175cmanda=52cm,itisevi- dent that magnetic deflection must be accounted for accurate profile inference.
B. Equilibrium profiles
We measure the equilibrium fusion proton emission pro- file in 300 kA non-reversed or F = 0 plasmas (the reversal parameter F is the ratio of the toroidal magnetic field at the wall to the average toroidal magnetic field). These plasmas are naturally free of the global tearing mode activity which manifest themselves as sawtooth crashes in standard reversed plasmas and are known to redistribute fast ions. This plasma is chosen for the measurement because several ms of quiescent plasma can be averaged over to obtain good counting statis- tics. The plasmas are also relatively free of x-ray producing fast electrons.
The results are shown in Fig. 5. The time histories of the average count rate from ∼5 similar discharges for 10 aiming angles are plotted in the left frame. The average profile, found by averaging the count rates in time from t = 31 to t = 35 ms, is plotted in the right frame with diamonds of corresponding color (consistent with the color code used for the orbits in Fig. 4). The measured proton emission profile is compared to
(Top frame) An example processed signal trace taken without a colli-