Temporal evolution of confined fast-ion velocity distributions measured by collective Thomson scattering in TEXTOR

Fast ions created in the fusion processes will provide up to 70% of the heating in ITER. To optimize heating and current drive in magnetically confined plasmas insight into fast-ion dynamics is important. First measurements of such dynamics by collective Thomson scattering (CTS) were recently reported [Bindslev et al., Phys. Rev. Lett. 97, 205005 2006]. Here we extend the discussion of these results which were obtained at the TEXTOR tokamak. The fast ions are generated by neutral-beam injection and ion-cyclotron resonance heating. The CTS system uses $100–150\mathrm{kW}$ of $110\text{−}\mathrm{GHz}$ gyrotron probing radiation which scatters off the collective plasma fluctuations driven by the fast-ion motion. The technique measures the projected one-dimensional velocity distribution of confined fast ions in the scattering volume where the probe and receiver beams cross. By shifting the scattering volume a number of scattering locations and different resolved velocity components can be measured. The temporal resolution is $4\mathrm{ms}$ while the spatial resolution is $\sim 10\mathrm{cm}$ depending on the scattering geometry. Fast-ion velocity distributions in a variety of scenarios are measured, including the evolution of the velocity distribution after turnoff of the ion heating. These results are in close agreement with numerical simulations.

Figure 1

(Color online) CTS scattering geometry in the TEXTOR tokamak. The probe enters the plasma in the horizontal midplane and the first receiver mirror is located $\sim 20\mathrm{cm}$ above. The resolved fluctuation wave vector ${\mathbf{k}}^{\delta }={\mathbf{k}}^{\mathrm{s}}-{\mathbf{k}}^{\mathrm{i}}$ is generally pointing towards the launch and receiver mirrors for the back scattering geometry used on TEXTOR.

Figure 2

Theoretical scattering function $\Sigma$ for a neutral-beam-heated TEXTOR plasma. The resolved velocity component makes an angle of 160° to the static magnetic field. The plasma parameters are $n_e=3\times {10}^{19}{\mathrm{m}}^{-3}$, $T_e=T_i=2\mathrm{keV}$, $n_D=2.5\times {10}^{19}{\mathrm{m}}^{-3}$, $n_H=2\times {10}^{18}{\mathrm{m}}^{-3}$, and $n_{\text{beam}\text{ion}}=3\times {10}^{18}{\mathrm{m}}^{-3}$.

Figure 3

(Color) Time trace of raw data sampled in six different channels. Red curves represent samples taken during gyro periods (gyrotron on, $\mathrm{CTS}+\mathrm{ECE}$), while blue are samples taken during ECE periods (gyrotron off, ECE). In the two upper plots (a), (b) the CTS component of the signal is visible. The two lower graphs (e), (f) show data from frequency channels where no CTS signal is expected. The green line is the reconstructed ECE level during the gyro periods. (c) shows a channel where no CTS signal is expected and in (d) only a small CTS level is expected. It is seen that the background ECE of all the channels have a similar temporal behavior including a strong perturbation due to sawtooth crashes at times $1.97\mathrm{s}$, $2.05\mathrm{s}$, $2.14\mathrm{s}$, and $2.23\mathrm{s}$.

Figure 4

(Color online) Spectral power density in six CTS channels during TEXTOR shot No. 89509.

Figure 5

(Color online) Contour plot of CTS spectral power density (a). The width of the CTS spectrum is seen to decrease after the ion heating is turned off at $t=2.2\mathrm{s}$. CTS spectrum at $t=2.3\mathrm{s}$ (after heating turn off) is shown in the upper plot (b) while that at $t=2.1\mathrm{s}$ (during heating flattop) is shown in the lower plot (c).

Figure 6

(Color online) TEXTOR shot No. 100467. Toroidal scan of the receiver beam viewing direction during an Ohmically heated plasma discharge. The probe beam was injected in the horizontal midplane with a toroidal angle of $-10°$. The receiver beam is seen to intersect the gyrotron beam in the time from $1.91\mathrm{s}\text{to}2.36\mathrm{s}$ corresponding to a toroidal receiver angle of $-13.75°$ to $-8.75°$. The scattering position was located at $R=1.8\mathrm{m}$, $z=0\mathrm{m}$ and gave rise to an angle of 110° between the magnetic field and the wave vector of the resolve fluctuations (i.e., close to perpendicular to $\mathbf{B}$).

Figure 7

(Color online) (a) CTS signal for a central overlap in the horizontal midplane with ${\mathbf{B}}_T\cdot {\mathbf{k}}^{\delta }>0$ and ${\mathbf{I}}_p\cdot {\mathbf{k}}^{\delta }<0$. A clear signature of the beam is seen in the spectral power density. The neutral beam injection (NBI) is turned off at $t=4.5\mathrm{s}$. The overlap geometry (top view) is shown in (b).

Figure 8

(Color online) (a) CTS signal for a central overlap in the horizontal midplane with ${\mathbf{B}}_T\cdot {\mathbf{k}}^{\delta }<0$ and ${\mathbf{I}}_p\cdot {\mathbf{k}}^{\delta }>0$. Here sawtooth oscillation are present at times $3.972\mathrm{s}$, $4.004\mathrm{s}$, $4.026\mathrm{s}$, $4.043\mathrm{s}$, $4.060\mathrm{s}$, and $4.077\mathrm{s}$. The overlap geometry (top view) is shown in (b).

Figure 9

(Color online) Outcome of an LSN fit to the measured data. (a) Measured data overlayed with theoretical model. (b) Model distribution. The dots are the nodes defining the fast ion distribution represented by the full curve. The bulk deuterium and hydrogen distributions are represented by dashed curves.

Figure 10

(Color online) Fast-ion velocity nodes with error bars using a broad prior (a) and a new prior with reduced width (b) assuming that the scaling and the impurity levels are near constant throughout the CTS measuring time.

Figure 11

(Color online) ${\mathrm{Log}}_{10}$ contour plot of obtained velocity distribution. The scattering geometry is described in Sec. 3 with a radial position of $R=1.67\mathrm{m}$ and a resolved direction of 113° to the magnetic field.

Figure 12

(Color online) (a) Time traces of the velocity distribution. (b) Time slices of the velocity distribution.

Figure 13

(Color online) Measured spectrum for discharge with low injected beam power (a) and with high injected beam power (b).

Figure 14

(Color online) Measured velocity distribution and overlayed Fokker-Planck simulation velocity distribution for different injected beam power for constant acceleration voltage. In both discharges the scattering volume was located at $R=1.81\mathrm{m}$. The resolved direction was 140° to the magnetic field.

Figure 15

(Color online) Fokker-Planck simulation of beam ions for TEXTOR shot No. 89509 at the NBI flat top at $t=2.1\mathrm{s}$. The contour levels are equispaced. The cylindrical coordinates $v_{\Vert }$ and $v_{\perp }$ represent the direction antiparallel and perpendicular to the static vacuum magnetic field. The direction of the projection measured by CTS, 67° to $v_{\Vert }$, is indicated by the arrow.

Figure 16

(Color online) Projection of the simulated energetic-ion test population shown in Fig. 15.

Figure 17

(Color online) Time evolution of the 1D projected Fokker-Planck simulation of beam ions for TEXTOR shot No. 89509 $\left({\log }_{10}{f}^{1D}\right)$.

Figure 18

(Color online) Direct comparison of measurement and simulation at superthermal velocities. As shown in Fig. 9b the ion population densities at $u=1.1$, 1.2 and $1.35\times {10}^6\mathrm{m}∕\mathrm{s}$ extend the bulk distribution. Good agreement during the slowing-down phase is found.

Figure 19

(Color online) Time evolution of the measured 1D velocity distribution $\left({\log }_{10}{f}^{1\mathrm{D}}\right)$. The fast ions seen at $u=1–1.5\times {10}^6\mathrm{m}∕\mathrm{s}$ decay once the ion heating is turned off at $\mathrm{t}=2.2\mathrm{s}$.