Page 3 - Demo

10-3 10-4 10-5 10-6 10-7
fluctuation profile e1
measurement locations
ne fluctuation spectrum
15 hydrogen 5 4
10 3 3
52 1 00
15 deuterium 5 4
0.5 0.0 -0.5
-0.5
766 0.8 511
0.6
255
0 0.4
-255
-511
r=0cm
r=15cm
r=30cm
r=45cm
0.9 ω/ωci
0.0 x (m)
0.5
0.8
1.0
1.1
1.2
B fluctuation spectrum
n
0 20 40 60 80 r (cm)
1
ω/ωci
10
-766 0.0
10 5
3 3 2
FIG. 3. (Top left) An idealized magnetic equilibrium (rigid rotor) shows the magnetic field strength (color map), separatrix (dotted line), and field null (dashed line), as well as the measurement lo- cations of the density (colored horizontal lines) and magnetic field (orange dot). Density fluctuation spectra show a clear peak near ωci at all radii, even those outside the separtrix (top right). Magnetic fluctuation spectrum shows that multiple harmonics of ωci are ex- cited (bottom left). The relative size of the density fluctuations peaks outside of the separatrix (bottom right).
In order to investigate the source of the fusion enhance- ment, we employ a high resolution, E∥M neutral particle en- ergy analyzer (NPA) with 39 energy channels per species to directly measure the evolution of both the bulk deuterium and injected hydrogen energy spectra.25 An average of 7 similar shots is shown in Figure 4. Early in time (t < 1 ms), there is a large energetic deuterium population due to the FRC forma- tion (the FRC is formed by the collision and merger of two su- per sonic compact toroids4). The energetic hydrogen popula- tion is born at 15 keV, but rapidly fills in as the beam-injected fast ions slow down and accumulate in the plasma. At about t = 1 ms, a broad tail appears in the deuterium channels, centered at 12 keV. The tail persists for several milliseconds until the FRC begins to decay away (these shots were non- optimized and therefore much shorter lived than sustained high performance shots, which last over 10 ms). The presence of the deuterium tail is additionally indicated by spectroscopic measurements of fast ion Dα (FIDA) emission,26 a diagnos- tic technique used to study both astrophysical plasmas (e.g., accretion disks) and fusion plasmas.27
The temporal behavior of the measured neutron rate, shown in Figure 2 to be much larger than the calculated thermonu- clear rate, trends very well with the temporal behavior of the rate calculated using the energy spectrum measured by the NPA. The rate is calculated 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 temperature is ignored here). The result is over-plotted on the measurement in the bottom panel of Fig- ure 4. This is proof that the neutron production is dominated by the high energy tail, rather than the thermal population.
0.2 0.7
1.0 0.8 0.6 0.4 0.2 0.0
0 0
1.0
0.8 measured 0.6 calculated
0.4
0.2 0.0
0 1 2 3 4 5 t (ms)
FIG. 4. Evolution of a discharge, from top; neutral hydrogen energy spectrum, neutral deuterium energy spectrum, measured (blue with grey error bars) and calculated (red) neutron flux. The calculated neutron flux is obtained from the deuterium energy spectrum.
SIMULATION AND THEORY
The experimental observations described above clearly in- dicate that the fast ions are exciting a wave which couples to the plasma to create a tail in the thermal ion energy distri- bution without any accompanying deleterious effects to bulk plasma confinement. 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 1D3V EPOCH particle-in-cell (PIC) code.28 In the simula- tion presented here, the ambient magnetic field points in the yˆ-direction and the wave vector kˆ points in the xˆ-direction (i.e., the initial mode is purely compressional). The condi- tion ∇ · Bˆ = 0 is explicitly enforced. The thermal plasma - deuteron ions and electrons - are sampled from Maxwellian distributions without any drift. The hydrogen beam is sampled from a drifting Maxwellian with drift velocity corresponding to the injection energy in the experiment, 15 keV. The beam is anisotropic such that E⊥ > E||. To resolve the modes ex- pected in the problem we have chosen a domain with length Lx = 1024λp, where λp is the ion skin depth, divided into Nx = 4096 cells with 800 particles per cell per species to keep the signal-to-noise ratio acceptable. Periodic boundary conditions for the fields and the particles are employed. A realistic mass ratio of mi/me = 1836 has been used.
The dispersion relation from a PIC simulation is shown in the top panel of Figure 5. When conditions approximating the SOL (i.e., β = 0.1) are used, many harmonics of the Ion Bern- stein wave emerge. This mode propagates nearly perpendicu- larly to the magnetic field at harmonics of the ion cyclotron frequency. When β is increased to 1 to simulate the core plasma, only the Alfve´n Ion Cyclotron (AIC) mode29 has large amplitude (not pictured). The AIC is a well-known mode driven by energy anisotropy, E⊥ /E|| , rather than a positive
3
δB (G)
y (m)
δ∫ndl / ∫ndl (10-4)
δ∫ndl (1011 cm-2)
neutrons (a.u.)
energy (keV)
energy (keV)
signal (a.u.)
signal (a.u.)
B (G)