Page 7 - Direct observation of ion acceleration from a beam-driven wave in a magnetic fusion experiment

NaTurE PHysIcs
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Methods
We present four experimental measurements (neutron flux, neutral particle energy spectra, and density and magnetic fluctuations), two calculations (thermonuclear fusion rate and energetic tail fusion rate) and one computer simulation (EPOCH PIC code). The methods for each are described in the following sections. The plasma under study is a unique FRC plasma formed by the supersonic merger of two theta-pinches and sustained with NBI. The techniques for creating the plasma are described in ref. 4.
Neutron measurements. The 2.45 MeV neutrons are a product of the deuterium– deuterium fusion reaction. Their mean free path in stainless steel (SS316L) is
2.6 cm (ref. 24), so the 1.3 cm confinement vessel is effectively transparent and the neutron detector can be conveniently located outside the vacuum boundary. The detector was mounted to the outside of the vacuum vessel near the north beam injection plane. The detection element was a 2 in. by 24 in. cylindrical plastic scintillator from Eljen Technology (EJ-200) coupled to a photomultiplier tube (PMT; model H6614-70 from Hamamatsu Corporation), designed for use in high magnetic fields. The PMT was operated with a bias voltage of 1.5–2.0 kV. The current signal output from the PMT was run through a 5 kΩ resistor to ground, and a unity gain operational amplifier (BUF634 from Texas Instruments) was used as a line driver to transmit the voltage signal to a D-TACQ analog-to-digital convertor with digitization rate of 1.5 MS s−1.
The detector was absolutely calibrated using two independent, in situ methods. The first method involved firing each of six deuterium-fueled neutral beams individually into a high-density (1014 cm3) deuterium gas target. The measured signal on the detector was then compared to the output of a Monte Carlo code used to simulate fast ions in the plasma. In this application, the magnetic field and plasma density in the simulation were set to zero so the code calculated the fusion rate due to the beam in the neutral gas. The second method was to insert a probe- mounted AmBe source into the vented vacuum vessel and measure the signal at
50 different locations. The two methods agreed well, giving a calibration factor of 2.4 ± 1.4 × 107 n s−1 V−1 and 2.6 ± 0.4 × 107 n s−1 V−1, respectively. The calibration procedure is detailed in ref. 14.
The time history of an average of the neutron rate over 57 shots is plotted in the black trace in Fig. 2c. A set of seven shots are plotted in the blue trace in Fig. 4c. The final data from the neutron detector are presented as two traces, red and black, from the staggered beam energy experiments plotted in Fig. 6c, as averages of three and four shots, respectively.
Neutral particle measurements. Neutral spectral flux measurements rely on energetic ions in the plasma that charge-exchange with neutral particles (H0) primarily concentrated at the outer boundary of the FRC plasma. These energetic, charge-exchanged particles are immune to the confining magnetic field of the experiment and promptly escape the system, a portion of which enter the NPA diagnostic system. The NPA view intersects the confinement chamber wall ~65 cm from the confinement chamber midplane, has an impact parameter of 49 cm,
and is oriented relative to the machine axis to match the expected energetic ion trajectories. The NPA view does not intersect any NBI ports.
On entering the diagnostic, charge-exchanged particles are re-ionized in a He-filled gas chamber (~3 mtorr), permitting analysis via electric and magnetic fields established inside the device. The particles are dispersed according to energy by a user-controlled magnetic field perpendicular to the particle trajectory. A user-controlled electric field parallel to the magnetic field disperses the particles according to mass. In this manner energy distributions of charge-exchanged deuterons and protons can be distinguished simultaneously as a function of time for the duration of the experiment.
Particles are registered on a dual-stage micro-channel plate (MCP) system, biased at −2 kV (~1 kV bias per stage). The MCP detection system is operated in current mode, producing an output current proportional to particle flux with ~107 gain. The MCP signal is amplified and digitized (1 MΩ gain, <10 μs response time) by an integrated device developed at TAE19.
Figure 4a,b shows the energy distributions for neutral hydrogen and deuterium, respectively, averaged over four shots. The calculated neutron rate shown in Fig. 4c is computed using the deuterium distribution data shown in Fig. 4b, as described in ‘Calculation of energetic ion-enhanced fusion rate’.
Magnetics measurements. Charged particle motion generates magnetic fields. High-frequency fluctuations in the magnetic field are detectable at the very edge of the plasma on the wall of the confinement vessel, but are stronger closer to the core plasma. We measured the edge magnetic fluctuations with wall-mounted coils and the interior fluctuations with an insertable magnetic probe. The wall-mounted coils are composed of three coils of wire for each orthogonal direction of magnetic field arranged in an azimuthal array of eight coils at z = 25 cm (ref. 25).
The θ direction is chosen for the fluctuation study because the equilibrium Bθ
is small, allowing small fluctuations to be resolved. Figure 6b shows the average wavelet spectrogram for two sets of shots (the spectrograms are averaged over coil number and shot number). The IDL routine WV_CWT with a 12th-order Morlet mother wavelet and dscale = 0.02, nscale = 500 and fmax = 2 MHz produces each spectrogram. The probe is composed of high-vacuum-compatible ceramic
chip inductors from Coilcraft CPS mounted on ceramic (Rogers 4003) printed circuit boards (PCBs) which produce a voltage in the presence of changing magnetic fields. Such a PCB is designed with two inductors (AE450RAA683GSZ and AE450RAA333GSZ) oriented so as to detect dBθ/dt and dBz/dt, respectively25. The inductors are standard 1812 surface mount chip size. The PCB is 3 in. long. The circuit board is mounted to an in-vacuum linear translation stage from Thermionics Inc. (FLMH-275-50-24) with a stroke length of 24 in. This system allows the probe to be positioned anywhere from flush with the vessel wall
(r = 70 cm) to a radius inside the scrape off layer of the plasma (r = 45 cm). The PCB assembly is protected from the plasma with a quartz tube. The probe signals are carried on screened, shielded twisted-pair cable terminated in 50 Ω and digitized by National Instruments digitizers (PXIe-5105) at a rate of 60 MS s−1. Figure 3c shows the discrete fast Fourier transform (performed with IDL routine FFT) of the partial time history (t = 0.5–1.5 ms) of a single shot with the probe inserted 3 cm from the vessel wall.
Density measurements. The density measurements shown in Fig. 3b,d are obtained from the FIR laser interferometer18. The system employs a CO pump
2 laser and two formic acid vapour FIR lasers (a probe beam and a reference
beam) with wavelength λ = 433 μm. The probe beam is split into four chords with impact parameters 0, 15, 30 and 45 cm. An additional two-colour CO2/HeNe interferometer is used to compensate for vibration.
The spectra plotted in Fig. 3 are obtained by performing a discrete fast Fourier transform on the detrended time histories of shot 43,393 from t = 1 to t = 3 ms using the FFT function in IDL. The peak in the spectra are fit with a four-term Gaussian (that is, Gaussian plus d.c. offset) using the GAUSSFIT IDL function. The profile (Fig. 3d) is then obtained by dividing the amplitude of the Gaussian by the mean value of the line-integrated density over the same time window.
Calculation of thermonuclear fusion rate. The thermonuclear fusion rate, plotted as the purple diamonds in Fig. 2c, is calculated using
12
R = 2 2πLFRC ∫ ni(r ) < σv > (Ti(r ))r dr, where ni is the ion density, which we obtain
by assuming that ni ~ ne and measure ne with interferometry18, using the central chord and dividing by the separatrix radius to give the central line-averaged density. The fusion reaction rate, <σv> is a known function26 of ion temperature, which we obtain from Ti = Ttot − Te, where Ttot is the total temperature derived from radial pressure balance (that is, FRC volume averaged pressure) and Te is measured with Thomson scattering27. Only two time points of electron temperature data are obtained per plasma discharge on C-2U, so the time history is built up by pulsing the laser at different times in each of 57 similar discharges. Finally, LFRC is the length of the FRC obtained from magnetic measurements25.
Calculation of energetic ion-enhanced fusion rate. The energetic ion-enhanced fusion rate (red curve in Fig. 4c) is calculated using R ~ ∫ dEf (E)σDD(E)v where f(E) is the NPA energy spectrum, σDD is the fusion cross-section26 and v is the energetic ion velocity (plasma temperature is ignored here). Because the NPA is not absolutely calibrated, magnitudes cannot be compared. The curve is scaled to best match the measured flux.
PIC simulation. EPOCH is a fully electromagnetic three-dimensional and three- velocity (3D3V) PIC code capable of running on 100,000 cores and able to self- consistently resolve the effects of electromagnetic fields on the electron and ion orbits and then feedback the orbits’ effects on the fields. As with many other PIC codes it may be decomposed into three components: particle pusher, particle/ current deposition and advancement of Maxwell's equations.
Particle push uses the Boris algorithm28. Particle/current deposition is carried out via the Esirkepov method29, and the standard finite-difference time-domain (FDTD) technique is used to advance Maxwell's equations numerically. E and B fields are specified on the staggered Yee mesh30. EPOCH uses high-order B-spline for the shape functions for particles. Each simulation particle is a macro-particle containing millions of physical particles. A fast Fourier transform of the time and space fluctuations of the fields on the grid is taken at the end of the simulation to analyse wave activity. This is the contour plot shown in Fig. 5a.
For a given set of physical parameters, the simulation approach of EPOCH
is compared with analytical and semi-analytical techniques. In the analytical approach, simple ω(k) relations (usually made in the approximation of a
cold plasma) are overlaid with the EPOCH results to verify general physical phenomena. In the semi-analytical approach, a more complicated dispersion relation, such as is given by the rank-three, kinetic dielectric tensor, is solved over a given domain of k and ω + iy using the winding number method.
In particular, for each of an array of k values, the dispersion relation is probed for solutions over a grid of sampling points in the complex plane for ω and y. One rectangular cell of four points is considered at a time. Using many intermediate sample points, as is necessary to provide smooth mapping, the dispersion relation is mapped over the closed contour formed by the four edges of the cell. If the winding number around the origin of the resulting mapped contour is non-zero, the original rectangular cell of sample points contains at least one solution. Once the full sample grid has been probed for all k values, the cells that contain solutions are themselves examined in a similar manner to refine the solutions.
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