Measurement of plasma density using nuclear techniques

The magnitude of a fusion reaction rate in a plasma depends strongly on the relative energy of the reacting plasma ions and less strongly on the ion number density. The ratio of two reaction rates, however, is less dependent on the relative velocities while retaining the linear dependence on the relative densities of the plasma ion species. In this manner, the ratio of t (d,n)a to d (d,n) 3He fusion reactions depends only on the ratio nJnd' so that tritium levels in a deuterium plasma can be determined from the d-t /d-d reaction ratio (nd:::::::ne)' Similarly, the density of 3He can be determined ~n a deuterium plasma from the ratio of 3He (d, p)a to d (d,n) 3He fusion reactions. Such measurements of the 3He density are of interest since they relate to the alpha ash removal problem expected on a tokamak reactor.


I. INTRODUCTION
Determination of the particle transport, edge recycling, and convective heat flow of a plasma all require measurement of the plasma ion density.While the electron density is routinely measured in tokamaks with microwave interferometry and Thomson scattering, the densities of the ionic constituents of a plasma are not easily measured.Possible ion density measurement techniques include mass sensitive charge exchange, \ which can determine the relative hydrogen and deuterium concentrations, charge exchange enchanced atomic spectroscopy, 2-4 which has determined fully stripped oxygen and carbon concentrations, as well as ordinary atomic spectroscopy, which is useful for determining high Z impurity concentrations.
In this paper, nuclear techniques are reviewed which make use of the d (d,n) 3He, 3He(d, p)a, and t (d,n)a fusion reactions to measure the densities of deuterium, 3He, and tritium.When these nuclear techniques are applicable they have the advantages of using naturally occurring emissions from the plasma (and are, therefore, nonperturbative), of allowing good time resolution, and of preferentially detecting emissions from the plasma center.Initial applications of these nuclear techniques on the PL T and PDX tokamaks at Princeton include: (I) Determination of the deuterium density in discharges that follow a switch in the plasma working gas from deuterium to hydrogen.These measurements indicate the fraction of plasma ions contributed by recycled gas and the rate of removal of deuterium from the vacuum vessel.
(2) Determination of the 3He density following short gas puffs of neutral 3He.These measurements indicate the 'He particle transport coefficients from the rise in 3He density following the puff, while the subsequent fall in density provides information on the 3He edge recycling and pumping rates.The rate of removal of 3He from the plasma relates to the alpha ash removal problem in a d-t reactor since 3He and 4He experience similar chemical interactions at the plasma-wall boundary.
(3) Planned determination of the tritium density following laser blow-off injection 6 of trace quantities of tritium.This experiment would be useful for determining tritium transport coefficients as well as for predicting the tritium inventory in d-t machines.

II. METHOD
The total fusion yield in a plasma is where / is the reaction rate, n \ is one reactant ion density, nz is the other reactant ion density, iT is the fusion cross section, V\2 is the relative velocity, the integral is over the plasma volume and the average, < ) is over the relative velocities between the I and 2 ions.The relative velocities of the reacting ion pairs are determined by the characteristics of the specific plasma and we note that there are two common situations: (a) the plasma ions are Maxwellian so that the fusion reactions are thermonuclear and (ov) is a unique function of the plasma ion temperature, or (b) the plasma ions include an energetic ion tail which produces the majority of the fusion reactions, the fusion reactions are no longer thermonuclear and (ov) is primarily determined by the characteristics of the energetic ion tail.
The use of Eq. ( I) to yield either the particle I or 2 density from the measurement of the reaction rate /12' requires accurate knowledge of the relative velocities V\2 since the fusion reaction cross section is strongly dependent on the relative velocity (Fig. 1).Small uncertainties in the relative velocity lead to large uncertainties in the inferred density.In fact, this was one major difficulty in early studies which determined deuteron densities in plasmas with low magnetic fields using the d (t,n)a fusion reaction rate caused by a diagnostic ion beam. 7• s An improvement occurs if the ratio of the rates of two reactions is measured.The ratio of the D-3He or d-t fusion rates to thed-d fusion rate can be less sensitive to the relative velocity of the reacting ion pairs than is the individual rate, while retaining the linear dependence on their densities.So far, it has turned out to be useful to create the fusion reactions with a deuterium neutral beam so that the fusion reac- tions are beam target. 9and the importance of variations in relative velocity are further reduced since (011) is determined almost entirely by the beam voltage.Creation of the fusion reactions by low power ( < 1 MW) neutral beams has the advantages that the injected beam ions have classical slowing down, confinement.and deposition 9 and that the detector count rate is easily chosen by selection of the beam voltage.
For beam-target reactions using a deuterium neutral beam 9 (3) are proportional to the density ratios since the behavior of the deuterium beam is common to all three reactions differing only in the cross-section weighting of the slowing down duration and the relative velocity.Specifically, this means that the beam species mix, neutral beam deposition, beam ion orbit losses on the first orbit, beam power, and beam slowing down rate do not enter into Eq.( 3).This would not be true if the beam ions suffered large losses on time scales faster than the cross-section weighted slowing down time or if the slowing down were complex as is possible in tokamaks under some circumstances.

Idd ~nd(O)sNB
The reduction in sensitivity to the relative velocity is greatest for R d _,.Using the Gammow forms for the cross sections 10  cases and, as expected from the above, is very insensitive to au even though each cross section individually is highly sensitive to the relative velocity.In this situation, the strong dependence of the cross section becomes a useful advantage of the technique since the fusion reactions tend to be localized in that part of the plasma containing the most energetic ions (e.g., the plasma center in tokamaks, Fig. 3) which is usually a region of considerable interest.
The ratio technique still retains a strong energy dependence in the determination of the 3He density, however, the ratio Rd_'He (Fig. 2) is about 20 times less sensitive to energy in the range 30 to 100 ke V than is the d-3He cross section (Fig. I).

III. EXAMPLES A. Deuterium density measurement
The application of the ratio technique to the measurement of the deuterium density consists of the comparison of the d (d,n) 3He fusion reaction rates from two discharges in which the relative velocities of the reacting ion pairs are thought to be the same (for example, when the charge exchange ion temperature is measured to be the same).In one of the discharges, the deuteron density is assumed to be given by nd ~ne' so that the microwave interferometer yields an approximation to the deuteron density.The deuterium density in the second discharge is then to have large uncertainties and are, therefore, not too useful.One example in tokamak experiments is when the working gas in the device is changed from deuterium to hydrogen I2 • 13  then the shot-to-shot decrease in the neutron emission can be used to determine the deuterium concentration.In this situation, the 2.S-MeV neutron emission form d (d,n) 3He can be used to monitor the decrease in deuterium concentration in the plasma or, effectively, the replacement of deuterium with hydrogen in the vessel components.The progression of the deuteron density was measured on a series of POX diverted discharges (Fig. 4) by the use of the steady-state thermonuclear neutron emission [Eq.4(b)], by the use of the beamtarget neutron emission [Eq.4(a)] created by a 30-keV diagnostic neutral beam injected at lOOms, and by the use of the H 2 , HO, O 2 peaks in the residual gas analyzer several seconds after the discharge, which is the usual way that such measurements are made.13By all three measurements, the deuteron density fell about a factor of 10 after about 30 discharges.The general agreement between the nuclear techniques and the residual gas analyzer indicates that the ratio of hydrogen isotopes in the plasma is similar to the ratio found in the walls l4 and to the molecular concentrations observed several seconds after the discharge.12 Using the thennonu- 4. Deuterium density for a series ofPDX discharges where the working gas was changed from deuterium to hydrogen.( X) thermonuclear reactions were used to measure n d • (e) beam target reactions were used to measure n d • (0) the residual gas analyzer was used to measure n d • The line is for a series of discharges on PLT reported in Ref. 12. PDX was operated with its four poloidal diverters for this series of discharges.The PLT vacuum walls had been preloaded with deuterium by glow discharge cleaning.The actual plasma conditions were similar (B~ -25 kG.I~ -400 kA, ii, -2X 1013 cm -3).
clear ratio [Eq. 4(b)] means that one should monitor T, on each discharge.but in reality such measurements were unavailable in this sequence.This means that 25% changes in T, that are possible must be considered as an uncertainty in the nd1n.determination.For shot 2. one obtains nd1n.
-0.3 --2 which is not too useful, but for shot 30 nd1ne -0.05 ~ 0.2 has comparable accuracy to the RGA technique.Using the beam-target ratio [Eq. 4(a)] means that one should monitor T. on each discharge to ensure a constant electron drag, but again such measurements were not available in this sequence.Reasonable expectations for the reproducibility of the plasma T. and the beam voltage imply that 50% uncertainties in nd1ne are obtained.Again.this measurement ability is useful only when nd1n, is small.
Clearly. the 3He and tritium density measurements should attain higher reliablility and accuracy since the ratios are measured on the same discharge.

B. Helium density measurements
The application ofEq.(2) to the measurement of3He densities 1~ consists of the comparison of the d-3 He reaction rate as measured by the 15-MeV proton emission 16 and the d-d reaction rate as measured by the 2.5-MeV neutron emission.Since there is still a strong relative velocity dependence in the ratio ofthe cross sections (Fig. 2).3He density measurements are made with beam-target fusion reactions induced by deuterium neutral beam injection so that the cross section is fixed by the beam voltage.In this case The principle -'He gas puffing experiments performed to date are on PLT 1 ' (132 cm major radius.28 or 38 cm minor radius.I ,,3.2 T toroidal magnetic field, 0.3 -.0.6 MA plasma current, 1.0-~5.0XlO13cm-3 Iine-averaged density, carbon limiters,titanium-gettered vacuum walls) during deuterium neutral beam heating (25 ~ 40 keV beam energy, .;;;1.2 MW beam power, tangential injection.)In these experiments the neutral beam duration was 300 ms.After 100 ms of injection.when the beam-heated plasma was in steady state.3He gas was puffed for 5 ms (the approximate gas valve exhaust time).The '~He thermalization time is S 0.5 ms so we expect the 3He to be in local thermal equilibrium with the plasma deuterons.The quantity of3He puffed was increased . .by increasing the gas puff duration.A direct correlation was observed between the magnitude of the electron density rise associated with the 3He gas puff, the 3He density measured by the nuclear technique, and the amount of JHe puffed into the vessel as determined by an ionization gauge (Fig. 6).The main uncertainty in using Eq. ( 5) to determine the 3He density is the absolute calibration of the IS-MeV proton detector.This calibration consists of determining the percentage of IS-MeV protons that escape the plasma on orbits that strike a surface barrier detector mounted at the vacuum ves-seL 17 While the absolute 3He concentration was determined to about a factor of2 accuracy, the determination of the time evolution of the relative 3He concentration from Eq. ( 6) is limited only by counting statistics.
The 3He gas puff was accompanied by an increase in the JHe II spectral line [Fig.7(al1 which was excited within 5 em  of the limiter radius (Fig. 3).The central 3He density with and without the gas puff is shown for a high density [Fig.7(bl1 and a low density [Fig.7(cl1 case.In the high density case, the 3He density rose rapidly following the gas puff and continued to rise for the duration of the neutral beam injection.In the low density case, the 3He density showed a similar initial rise which peaked and then decreased steadily.These two cases are to be compared to the solutions of a cylindrical diffusion equation with constant diffusion coefficient and a delta-function initial density at a radius of 35 cm.The time evolution of the average 3He density inside 20 cm is shown for reflecting wall [Fig.7(d)] and absorbing wall [Fig.7(e)] boundary conditions.The initial density rise in this model is similar for the two boundary conditions, but the long time behavior differs markedly as particles are taken out of the system by the absorbing wall.
The rise in the central 3He density following a short (5 ~~ 10 ms) 3He gas puff at the plasma edge [Fig.7(a)] indicates that the transport time oeHe ions to the plasma center is (20 ± 10) ms, increasing modestly with density (Fig. 8) and toroidal magnetic field (Fig. 9).This time scale is comparable to previous spectroscopic measurements for the transit times of moderate and high Z impurity ions in PL T. 18 The inward transport time is consistent with a diffusion coefficient of (4 ± 2) X 10 3 cm 2 /s or an inward directed velocity of (2 ± 1) X 10 3 cm/s, which are -10 ---<0 10 2 times larger than the corresponding neoclassical particle diffusion coefficient or Ware pinch velocity.• with strong recycling and poor lHe pumping at the plasma edge.However, the pumping rate is about ten times faster than for neutral 3He to be removed by the PLT vacuum pumps.The helium exhaust process was stronger at low plasma density, which may have been caused by a change in the plasma edge conditions.The residual 3He density left from the previous discharge was approximately 1/2 -+ 1/5 of the maximum 3He density in that discharge (Fig. 10), indicating that considerable 3He was retained in the vessel walls.
Co + counter neutral beam injection caused higher residual 3He densities than either Co or counter injection alone (at 1/ 2 of the beam power).

c. Tritium density measurements
Density measurements by nuclear diagnostics is best utilized when determining small tritium concentrations in predominantly deuterium plasmas (n,lnd:::::: 1O~4 -+ IO~ 1).The attractiveness of the tritium measurement is that since the triton and deuteron have the same Coulomb barrier, the ratio of the d~t / d-d cross sections is about constant independent of relative velocity.Thus, (7) independent of the origin of the fusion reactions.Furthermore, since the t (d,n)a cross section is large, it seems likely that sensitive tritium density measurements are possible.Experimentally, the difficulty is in selectively measuring 14-MeV neutron emission levels in the range 1O~2 -+ 10 times the 2.5-MeV neutron emission levels.Neutron spectrometers 18 and threshold detectors l7 • IK are thought to be useful for such measurements.Experiments are planned on the PL T tokamak involving the laser blow-off injection of tritiated titanium in order to determine the inward tritium transport, the tritium exhaust, and the tritium removed by subsequent plasmas.Injection of 1 -+ 10 mCi of tritium should be detectable.
FIG. 1. Reactivities for the d Id,n) 'He and 'Held, pIa fusion reactions as a f"wtion of deuteron l:n~rgy for beam-target reactions.

FIG. 2 .
FIG. 2. Ratio of the d-'He to the d-d fusion reaction rates as a function of deuteron energy for beam-target reactions.
I~d(a) nd = n: -,-I ddJ.Vac.Sci.Technol.A, Vol. 1, No.2, Apr ....,June 1983    (b) n~ = n;""!!:!depending on (a) if the reactions are of a beam-target nature caused by energetic ions from neutral beam heating or (b) if the reactions are of a thermonuclear nature as caused by the bulk plasma ions.Due to the n',; ~n;' assumption and the requirement that (au)' = (au)", applications ofEq.(4) tend mJddlw s +3T, 7Id-d mJ d _'He,lw 8 +7T, 3(5)If we arrange for n'Hjn e He small and for nd1ne to be a constant.then the central~He density is n, (t) = Cn (t I Id_'He(t) -'He density can be obtained without accurate determination of C so long as Zeo-.W B' and T, remain constant with time.Thus.one useful application of3He density measurements is when small quantities of 3He are puffed into the edge of a tokamak.As a result of the 3He puff of Fig.5 the d-3He reaction rate increased by about a factor of 5 while the d-d reaction rate decreased by about 20% (due to increased electron drag on the energetic injected beam ions.) FIG. 5. Time evolution ofthed-d reaction rate as measured by the 2.5-MeV neutron emission.the d-'He reaction rate as measured by the 15-MeV proton emission, and the electron density.The reactions are beam-tartet induced by a 35-kV deuterium neutral beam.The lO-ms'He gas puff caused Ii, to increase by 10%.thed-'He rate to increase by a factor of5, and the dd rate to decrease by 20%.
FIG. 6.The line average 'He density rise (nuclear technique) vs the amount of 'He puffed into the PL T vessel.The (..:l ) points are one-half the electron density rise resulting from the 'He puff.
FIG. 8. 'He penetration IT R) and exhaust IT,) times vs line average density.