Page 2 - Direct observation of ion acceleration from a beam-driven wave in a magnetic fusion experiment

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Fig. 1 | illustration of the FRC. The FRC is shown as a solid body (with cut- away) with closed field line surfaces (red shells) embedded in the mirror plasma (yellow tubes). A sample 7 keV fast ion trajectory is shown in blue.
on the densities and temperatures of the reactants and the reaction cross-section. Two absolutely calibrated14 scintillator-based neutron detectors are located close to the vessel wall on the atmosphere side. The FRC plasma is pure deuterium and the neutral beams are pure hydrogen. There is therefore no beam-plasma component to the neutron production, and neutrons are produced only due to fusion reactions between plasma ions themselves. That the beams are deu- terium-free is confirmed experimentally by firing the beams into the deuterated vessel wall and measuring zero neutron signal.
Shown in Fig. 2c is the shot-averaged measured rate (black line with salmon error bars) and the calculated thermonuclear rate (pur- ple diamonds). It can be seen that the measured rate exceeds the thermonuclear rate from very early on in the discharge. The ther- monuclear rate is calculated as R= 21 2πLFRC ∫ni(r)2 <σv>(Ti(r))rdr where LFRC is the length of the FRC obtained from magnetic mea- surements of excluded flux15, ni(r) is the ion density, which we obtain from Abel-inverted interferometry measurements16 of ne(r) and assuming quasi-neutrality (ni ~ ne). The ion temperature, Ti(r), is calculated using radial pressure balance to determine the total internal pressure and subtracting the contribution for electrons, whose temperature is measured with Thomson scattering (see Methods for details).
The measured neutron rate clearly diverges from the calculated rate very early in time. This timescale is much faster than the tim- escale for collisional heating of plasma ions by beam particles. A fast test particle with velocity between the ion and electron thermal velocity must slow to the critical energy before it will have a signifi- cant probability of pitch angle scattering on plasma ions (the critical energy is the energy at which power flow to the ions and electrons is equal)17. In our case, the injected ions have, Efi = 10Ecrit and therefore two to three e-folding times (2–4ms) must pass before significant energy flow to the ions is expected.
In addition to measurements of the neutron flux, we measured the intermittent magnetic and density fluctuations near the plasma ion cyclotron frequency. The magnetic fluctuations were measured ~10 cm inside the wall in the mirror plasma with a high-time-reso- lution magnetic probe and the density fluctuations with far infrared (FIR) interferometry18 from four different viewing chords (impact parameters r = 0, 15, 30, 45 cm). The magnetic probe measurements revealed mode activity at the fundamental and higher harmonics of the ion cyclotron frequency (Fig. 3c). The density fluctuations reveal that there is an electrostatic component to the mode and that it is not confined to the FRC, as the fluctuations appear on the r = 45 cm chord, which does not intersect the FRC. In fact, the rela- tive size of the line-integrated fluctuations (that is, δ ∫ ndl∕ ∫ ndl) is largest on this most-outboard chord, outside the separatrix.
To investigate the source of the fusion enhancement, we used a high-resolution, E||B neutral particle energy analyser (NPA) with 39 energy channels per species to directly measure the evo- lution of both the bulk deuterium and injected hydrogen energy
spectra19. The line of sight of the NPA has a large impact param- eter (b=49cm) so it does not measure ions in the FRC core, and with a minimum energy of 1 keV, the detector is not sensitive to the thermal population. An average of seven similar shots is shown in Fig. 4. Early in time (t < 1 ms), there is a large energetic deuterium population due to FRC formation (the FRC is formed by the colli- sion and merger of two supersonic compact toroids4). The NBI fast hydrogen population is born at 15 keV, but rapidly fills in as the fast ions slow down and accumulate in the plasma. At about t = 1 ms, a broad tail appears in the deuterium channels, centred at 12 keV. The tail persists for several milliseconds until the FRC begins to decay away. The deuterium ions do not show the characteristic slow- ing down that the injected hydrogen ions do because at this large radius the more massive deuterium ions are not confined. It is also important to note that the amplitude of the NPA signal from the tail is comparable to that of the signal from the injected beam ions, so nuclear elastic scattering or ‘knock-on’20 can be excluded as a candidate mechanism.
The temporal behaviour of the measured neutron rate trends very well with the temporal behaviour of the rate calculated using the energy spectrum measured by the NPA. This stands in stark contrast to Fig. 2, where the temporal behaviours of the calculated and measured rates differ as greatly as the amplitudes. The rate is calculated here assuming the fusion collisions are dominantly between energetic tail ions and bulk plasma ions as R ∼ ∫ dEf (E)σDD(E)v where f(E) is the NPA energy spectrum, σDD is the fusion cross-section, and v is the ion velocity (plasma tem- perature is ignored here). Although the tail is measured to exist in the tenuous mirror plasma, the low magnetic field means that the fast ions have large orbits and can travel into the FRC where the larger plasma ion density makes fusion more likely. The result is over-plotted on the measurement in Fig. 4c. The excellent agree- ment between the two curves is compelling evidence that the neu- tron production is dominated by the high-energy tail interacting with the thermal plasma, rather than from within the thermal population itself.
It should be noted that the number of suprathermal ions is small, ~1% of the background ion population based on the neutron flux. The energy per particle, however, is large (~12keV), so the total energy is therefore not insignificant. At ~500 J, the energy in the tail is approximately 10% of the total thermal energy of the plasma. The characteristic time for the tail to grow up is ~1ms, a time during which 10kJ of neutral beam power can accumulate in the plasma. This means ~5% of the injected beam energy ends up in the tail of the energy spectrum of the background ions.
Simulation and theory
The experimental observations described above clearly indicate that the fast ions are exciting a wave that couples to the plasma ions to create a tail in the energy distribution without any accompanying deleterious effects to bulk plasma confinement (there is no observ- able increase in magnetic flux or particle inventory decay rates). What is not clear from the measurement is whether this is a global or local phenomenon, and, if local, where in the plasma the mode is most active. For this, we turn to simulation.
We model the problem as an initial value problem in the PIC code EPOCH21. In the simulation, the wavevector is perpendicular to the magnetic field. The thermal plasma is Maxwellian without any drift. The hydrogen beam is a drifting Maxwellian with drift velocity corresponding to the injection energy in the experiment, 15 keV (see Methods for more details).
The dispersion relation from a PIC simulation is shown in Fig. 5a. When conditions approximating the mirror plasma are simulated (that is, when β, the ratio of the plasma pressure to the magnetic pressure is 10%), many harmonics of the ion cyclotron frequency emerge and the mode is identified as the Ion Bernstein
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