Fusion product studies via fast ion D–D and D–³He fusion on JET

The 3rd harmonic ICRH-acceleration of D beam in D plasma [9] was established on JET as an effective technique for creating a population of D ions in the MeV energy range, with the highest possible D–D fusion yield per unit of heating power. The peak performance of the RF generators on JET is achieved at $f$ ~ 51 MHz. Accordingly, this frequency determines the best choice of the toroidal magnetic field of B_T  ≈  2.24 T for maximizing coupling ICRH power to NBI-produced ions close to the magnetic axis. Figure 2 shows the geometry of the ICRH resonances satisfying $f=n{{f}_{\text{Ci}}}$, where $n$ is a harmonic of the ion cyclotron frequency, and ${{f}_{\text{Ci}}}$ is the local cyclotron frequency of ion species $i$. As figure 2 shows, the resonance line $f=3{{f}_{\text{CD}}}$ passes through the magnetic axis at the field and frequency chosen, while the possible undesirable absorption mechanisms by hydrogen resonances, $f={{f}_{\text{CH}}}$ and $f=2{{f}_{\text{CH}}}$ are minimised by putting the $n=2$H resonance outside the torus, and the fundamental H resonance—in the cold plasma edge region at the high field side of the machine. Still, the proximity of the fundamental H resonance close to the first wall of the machine made the machine safety an issue as some H ions are always present in the machine and their acceleration to high energy could cause hot spots at the first wall, due to wide orbits. For assessing carefully the effects of the undesirable H-minority resonance close to the inner wall, five discharges were first made on JET with progressively increasing ICRH power, from 2.9 MW to 4.2 MW, at decreasing magnetic field from 2.33 T to 2.24 T. It was found that the H-minority resonance is not an issue as long as RF waves launched from the outer side of the torus couple well to the D beam ions. Only when NBI power was below the prescribed value, ~1.4 MW in discharges #86776 and #86777, did the beam not provide sufficiently strong absorption of ICRH power (which was about ~4 MW), and the discharges disrupted. At higher NBI power, no problem with the machine safety occurred.

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The effect of D beam acceleration in D plasma gives a spectacular increase in D–D fusion yield with a significant increase in the energy of the D–D neutrons born. This effect could be best observed with neutron spectrometers, e.g. with the time-of-flight TOFOR spectrometer [3], which was tested on JET more than other spectrometers in D–D plasma. The TOFOR device is placed well above the JET machine, with the line-of-sight passing through the magnetic axis perpendicular to the magnetic field. Since ICRH mostly increases the beam ion velocity perpendicular to the magnetic field, the interpretation of the D–D neutron spectrum does not involve the beam velocity parallel to the magnetic field, and is relatively straightforward. In particular, it is possible to establish a correspondence between maximum energy of the projectile D ions and maximum energy of the D–D neutrons resulting from the fusion of these projectile ions and thermal D plasma. Figure 3 shows an example of JET discharge (pulse #86459 with B_T  =  2.26 T, I_P  =  2.16 MA), with the combined synergetic NBI and 3rd beam harmonic ICRH, with the TOFOR measurements of D–D neutrons made at different times. It is seen in figure 3 that by adding ~3 MW of ICRH power at 3rd harmonic to ~4.5 MW of D NBI in D plasma, it was possible to increase the yield of D–D neutrons by a factor of ~10. Indeed, the TOFOR measurements show much lower yield of D–D neutrons during NBI-only heating (see figures 3(a) and (b)) phase than during NBI  +  ICRH phase (see figures 3(c) and (d)). Furthermore, the fastest time-of-flight decreases significantly, in line with the expected broadening of the energy spectrum of the D–D neutrons. Note, that the time-of-flight of D–D neutrons measured with TOFOR, depends on the neutron energy as ${{\tau}_{\text{TOF}}}\propto E_{n}^{-1/2}$ giving a value of ~65 ns for 2.5 MeV neutrons, and much shorter time of ~45 ns for 5 MeV neutrons.

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Detailed studies of high-harmonic ICRH are not presented here: they have been separately reported in [9–11] of this Special Issue. For understanding the key points of these studies, we only give some qualitative estimates relevant to our experiment. The RF power density, ${{p}_{\text{abs}}}$, absorbed by the ions with mass $m$ and distribution function $f$ resonating with the wave launched, is given by [9]:

$$\begin{eqnarray}&&{{p}_{\text{abs}}}=-{\int}^{}mV_{\bot}^{2}{{D}_{\text{RF}}}\frac{\partial f}{\partial {{V}_{\bot}}}\text{d}{{V}_{\bot}},\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&{{D}_{\text{RF}}}\propto {{\left[{{E}_{+}}\,{{J}_{n-1}}\left(\frac{{{k}_{\bot}}{{V}_{\bot}}}{{{\omega}_{\text{Ci}}}}\right)+{{E}_{-}}\,{{J}_{n+1}}\left(\frac{{{k}_{\bot}}{{V}_{\bot}}}{{{\omega}_{\text{Ci}}}}\right)\right]}^{2}},\end{eqnarray} \tag{ 5 }$$

where ${{V}_{\bot}}$ is the ion velocity perpendicular to the magnetic field, ${{\omega}_{\text{Ci}}}=2\pi {{f}_{\text{Ci}}}$ is the ion cyclotron frequency, ${{k}_{\bot}}$ is the perpendicular wavenumber of the fast wave launched, ${{J}_{n-1}}(x),{{J}_{n+1}}(x)$ are the Bessel functions of first kind. Fast magnetosonic wave launched by the RF antenna is an elliptically polarized mode and its electric field can be decomposed as a sum of two components: the left-hand polarized component ${{E}_{+}}$, which rotates in the ion direction, and the right-hand polarized component ${{E}_{-}}$ (counter-rotating). For $n\geqslant 2$, the relation between ${{E}_{+}}$ and ${{E}_{-}}$ is approximately given by ${{E}_{-}}/{{E}_{+}}=(n+1)/(n-1)$. Among the Bessel functions, only Bessel function of the zeroth order has a finite value at zero argument, ${{J}_{0}}(0)\ne 0$. This case corresponds to $n=1$, i.e. $\omega ={{\omega}_{\text{Ci}}}$ fundamental resonance. In our case, such fundamental resonance can be relevant to some H minority ion acceleration starting from thermal velocities, ${{V}_{\bot}}\to 0$. As a result of such H-minority ICRH, the well-known Stix distribution function is generated [12]. For higher harmonics, $n\geqslant 2$, the absorption mechanism requires a finite value of the argument ${{k}_{\bot}}{{V}_{\bot}}/{{\omega}_{\text{Ci}}}$ in the Bessel functions of a higher order, i.e. the high-harmonic effect relies on a finite Larmor radius. For providing effective 3rd harmonic ICRH power absorption in our experiment, a D beam with injected supra-thermal energy of ~100 keV was used as a seed absorber of the ICRH power. As the beam energy increases from ~100 keV to ~1 MeV during the interaction with RF waves, the beam absorption of RF power increases too, from ~10% to ~80% [10], achieving the highest value at the maximum of the ${{D}_{\text{RF}}}$ determined by Bessel functions ${{J}_{4}}\left({{k}_{\bot}}{{V}_{\bot}}/{{\omega}_{\text{CD}}}\right)$ and ${{J}_{2}}\left({{k}_{\bot}}{{V}_{\bot}}/{{\omega}_{\text{CD}}}\right)$. Further increase in the beam energy gives, however, Larmor orbit width larger than the wave-length of the launched RF wave. When the Larmor radius becomes large enough to satisfy ${{k}_{\bot}}{{V}_{\bot}}/{{\omega}_{\text{CD}}}\approx 5.1$, the function ${{J}_{2}}\left({{k}_{\bot}}{{V}_{\bot}}/{{\omega}_{\text{CD}}}\right)\to 0$, and for ${{k}_{\bot}}{{V}_{\bot}}/{{\omega}_{\text{CD}}}\approx 7.6$—the function ${{J}_{4}}\left({{k}_{\bot}}{{V}_{\bot}}/{{\omega}_{\text{CD}}}\right)\to 0$, thus making ${{D}_{\text{RF}}}$ small and effectively cutting off the absorption of the RF power if the D tail energy becomes too high. To estimate the velocity at which this occurs, one could take into account the dispersion equation of the launched fast wave to find ${{k}_{\bot}}\approx \omega /{{V}_{\text{A}}}=3{{\omega}_{\text{CD}}}/{{V}_{\text{A}}}$. By substituting this value of ${{k}_{\bot}}$ in the expression ${{k}_{\bot}}{{V}_{\bot}}/{{\omega}_{\text{CD}}}\approx 7.6$, one finds that the maximum velocity, that can be achieved by D ions, is determined by Alfvén speed ${{V}_{\text{A}}}$ as follows:

$$\begin{eqnarray}&&V_{\bot}^{\max}\approx 2.5\centerdot {{V}_{\text{A}}}\equiv 2.5\centerdot {{B}_{0}}/\sqrt{4\pi \underset{i}{\sum}\,{{m}_{i}}{{n}_{i}}}.\end{eqnarray} \tag{ 6 }$$

For typical ion density used in the JET-ILW experiment with D plasma, ${{n}_{\text{D}}}(0)\approx 4\times {{10}^{13}}\,\text{c}{{\text{m}}^{-3}}$, this cut-off velocity is $V_{\bot}^{\max}\approx 1.4\times {{10}^{9}}$ cm s⁻¹ corresponding to fast D energy of ~2 MeV. Due to significant differences in plasma density scenarios in JET-CW and JET-ILW, a density variation from ${{n}_{\text{e}}}(0)\approx 3\times {{10}^{13}}\,\text{c}{{\text{m}}^{-3}}$ (JET-CW pulse #73216) to ${{n}_{\text{e}}}(0)\approx 6.4\times {{10}^{13}}\,\text{c}{{\text{m}}^{-3}}$ (JET-ILW pulse #86762) at the peak fusion yield was achieved during the 3rd harmonic experiments. With such density spread, it was possible to assess the density dependence (6) in the maximum velocity of the ICRH-accelerated D beam ions. This D velocity dependence on plasma density was deduced from broadening of D–D neutron spectrum up to $\cong$4–6 MeV in the TOFOR measurements [13]. Due to the fixed value of the magnetic field, plasma density is the only parameter that determines the maximum velocity of D ions accelerated with the high-harmonic ICRH, providing these D ions are still confined in the plasma.

Considering now the fast ion energy content, $E={{n}_{\text{f}}}{{T}_{\text{f}}}V$, where $V$ is volume occupied by the fast ions, and ${{n}_{\text{f}}},{{T}_{\text{f}}}$—spatially averaged density and temperature of the fast ions, the energy balance reads

$$\begin{eqnarray}&&\frac{\text{d}E}{\text{d}t}=-\frac{2E}{{{\tau}_{\text{SD}}}}{{\left[1+\left(\frac{{{E}_{\text{crit}}}}{E}\right)\right]}^{3/2}}+{{P}_{\text{RF}}},\end{eqnarray} \tag{ 7 }$$

where ${{\tau}_{\text{SD}}},{{E}_{\text{crit}}},{{P}_{\text{RF}}}$ are the slowing down time of the fast ions, the critical energy of the ions, and RF power. In the steady-state, $\text{d}E/\text{d}t=0$, and for typical condition ${{E}_{\text{crit}}}/E\ll 1$, one obtains [12]:

$$\begin{eqnarray}&&{{n}_{\text{f}}}\centerdot {{T}_{\text{f}}}\centerdot V=\frac{1}{2}{{P}_{\text{RF}}}\centerdot {{\tau}_{\text{SD}}}.\end{eqnarray} \tag{ 8 }$$

In the expression above, the tail temperature of the fast ions ${{T}_{\text{f}}}$ could be controlled by choosing plasma density as explained above. For maximizing ${{n}_{\text{f}}}$ at given ${{T}_{\text{f}}}$, one could increase either ICRH power, or ${{\tau}_{\text{SD}}}$ via increasing electron temperature ${{T}_{\text{e}}}$. Both options were explored, with the D–D fusion yields being significantly different in JET with carbon wall and with ILW delivering quite different electron temperatures and densities.

Analysis of the experiments with the suite of ICRH-modelling tools PION, SELFO, SELFO-light, TORIC, and SPOT/RFOF presented in [9–11] takes into account effects associated with the distribution functions, geometry and plasma and equilibrium profiles not discussed above, but very important for the quantitative assessment of the fusion rates. The use of multiple diagnostics in the experiment described presented an excellent validation test-bed for all the codes involved in the modelling. In general, the modelling results [9–11] are found to agree with the measured neutron and gamma-ray spectra and profiles, as well as with global plasma parameters and fast ion diagnostics measurements. This agreement indicates that the beam acceleration by ICRH and fast ion confinement are relatively well understood.

The yield of D–D neutrons and the neutron emission spectra measured in the experiments with 3rd harmonic ICRH of the D beam were the focus of the fusion product studies. In JET with CW, neutron rates up to $R_{\text{n}}^{\text{DD}}\approx 1.1\times {{10}^{16}}$ s⁻¹ were achieved at the input power of 4.7 MW NBI  +  2.7 MW ICRH only (pulse #74941), and JET with ILW delivered neutron rates up to $R_{\text{n}}^{\text{DD}}\approx 0.8\times {{10}^{16}}\,{{\text{s}}^{-1}}$ at 6.5 MW NBI  +  4 MW ICRH (pulse #86775). These neutron rates are quite significant when one considers that the JET record in D–D fusion was $R_{\text{n}}^{\text{DD}}\approx 5.5\times {{10}^{16}}$ s⁻¹ achieved in a discharge with internal transport barrier in 1990th (pulse #40554 with 18.5 MW NBI  +  6 MW ICRH). The high neutron rate allowed TOFOR measurements of D–D neutron spectrum to be performed with time resolution of ~50 ms [14]. Figure 4 shows the neutron energy spectrum deduced from the TOFOR measurements of the neutron time-of-flight, in one of the JET discharges with CW (pulse #74937 with B_T  =  2.24 T, I_P  =  2.17 MA). The maximum energy of the fusion-born neutrons is well above 2.5 MeV approaching ~5 MeV. The energy spectrum of fast D ions was deduced then from the energy spectrum of measured D–D neutrons. It was found that D ions must have been accelerated to  >2 MeV or so in order to generate the measured D–D neutron spectrum, in agreement with the estimate (6) showing the cut-off energy of the ions. Furthermore, the dependence of the maximum D–D neutron energy on plasma density was established and described in detail in [13] thus suggesting the density of plasma as a possible tool for controlling the energy spectrum of D–D neutrons.

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Acceleration of D ions to the MeV energy range was further confirmed by gamma-spectrometry, the scintillator probe measurements, and excitation of Toroidal Alfvén Eigenmodes (TAEs) in these JET discharges. Due to the carbon impurity present in JET plasmas with CW, intense gamma-rays were generated in nuclear reaction ¹²C(D, pγ)¹³C at specific energy ~3.1 MeV as figure 5 shows. This reaction requires kinetic energy of D ions exceeding ~700 keV, and for the set of JET discharges performed with CW a best fit procedure for the gamma-spectra suggested averaged temperature of ~400 keV for the D fast ions.

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Furthermore, the scintillator probe located just below the outer mid-plane of the machine was detecting loss of fast ion as figure 6 shows. The range of the Larmor radii measured by the scintillator for these losses, corresponds to D ion energies from ~780 keV to ~1.35 MeV, with possible higher energy lost ions present, but exceeding the maximum size of Larmor orbits measured with this probe.

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A very high activity of TAEs in the frequency range of ~150–250 kHz, with toroidal mode numbers from 3 to 8, was in these JET discharges. These were identified to be excited by precessional resonances between TAEs and trapped D ions of MeV energy range. This TAE activity and subsequent monster sawtooth crashes were investigated in detail in [15] based on the TAE data together with the gamma-ray spectrometry and 2D gamma-ray profile measurements using carbon as the main impurity.

The experiment with 3rd harmonic ICRH acceleration of D beam was recently performed on JET with ILW. The all metal wall does require a higher plasma density at the beginning of the discharges, in order to prevent tungsten accumulation when the plasma forms. As a result, ${{T}_{\text{e}}}$ values are lower thus affecting the fast ion slowing-down time and the fusion yield. Figure 7 shows comparison of two JET discharges, with carbon wall (#74941, B_T  =  2.24 T, I_P  =  2.18 MA) and with ITER-like wall (#86461, B_T  =  2.26 T, I_P  =  2.16 MA), in which NBI and ICRH power levels were very similar. The lower ${{T}_{\text{e}}}$ in the case of JET with ILW is seen, with the D–D fusion rate in the case of ILW about 40% lower than that obtained with the C wall.

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Summarising this section, we demonstrated that the use of 3rd harmonic ICRH-acceleration of D beam ions in D plasmas gives a distribution function of D ions with maximum energy ~ 2MeV, which cuts off sharply then. This distribution function delivers fast ion D–D fusion with high neutron rates, up to ~1.1  ×  10¹⁶ s⁻¹ in JET-CW case, and ~0.8  ×  10¹⁶ s⁻¹ in JET-ILW case, and with D–D neutron energy spectrum spreading up to ~5 MeV. In this scenario, beam-target D–D neutrons dominate and the energy spectrum of D–D neutrons can be controlled by plasma density, while the number of fast D ions and resulting D–D neutrons can be controlled by ${{T}_{\text{e}}}$ and P_RF.

There were two main aims of this experiment. First, investigation of some material samples subjected to the flux of ~15 MeV protons born in the D–³He fusion was performed [19]. For that, a reciprocating probe was used allowing for the accumulation of the proton bombardment effects over many JET discharges. For the purpose of maximising prompt losses arising from drift orbit excursions of the fusion-born protons, currents as low as ~1.5 MA were used. For clearer interpretation of the results, a slowing-down distribution of the beam was required, with the cut-off of the fast D energy around the beam injection energy [19]. Second, the problem of assessing the yield of D–³He fusion via a weak secondary reaction was addressed:

$$\begin{eqnarray}&&\text{D}\,+\,_{{}}^{3}\text{He}\to \,_{{}}^{5}\text{Li}+\gamma \left(\text{16}.\text{4}\,\text{MeV}\right).\end{eqnarray} \tag{ 9 }$$

The rate of D–³He fusion measured from the ~16.4 MeV γ-rays produced in the reaction (9), was used in [18] for assessing the record-high fusion rate. In the case of D beam injection into the D–³He mixture, such type of measurement relevant to D–³He fusion could be validated against the D–D fusion generated with the same beam in the same plasmas. The neutron/gamma spectrometry as well as 2D neutron/gamma camera could be used for providing such validation.

In these discharges, up to 18.5 MW of NBI power was injected into plasmas with ³He density gradually increasing, discharge-by-discharge, from ${{n}_{\text{H}{{\text{e}}^{\text{3}}}}}/{{n}_{\text{e}}}=0$, to ${{n}_{\text{H}{{\text{e}}^{\text{3}}}}}/{{n}_{\text{e}}}\approx \text{3}0\%$. The depletion of the D–D neutron rate provided crude estimate of the total D–³He fusion rate, while the 2D neutron camera and CX measurements of He profiles were used for obtaining the information on the spatial profiles. Figure 8 shows the results of the D–D and D–³He fusion source profiles calculated with the FIDIT code [20].

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The data on 16.4 MeV gamma-rays described by (9) was collected successfully showing that the D–³He fusion power was proportional to the power of D NBI, and the maximum D–³He fusion power achieved was ~15 kW (see figure 9) in JET discharge with ${{n}_{\text{H}{{\text{e}}^{\text{3}}}}}/{{n}_{\text{e}}}\approx \text{3}0\%$ (pulse #72631, B_T  =  2.5 T, I_P  =  1.8 MA).

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This is the most common technique of obtaining D–He³ fusion on JET, which was also used in the record-high D–³He fusion yield discharges [18]. For the ICRH power available, ${{P}_{\text{RF}}}$  ⩽  5.5 MW, quite significant fusion power yield of ~100 kW was achieved in JET discharge #73206 with B_T  =  3.45 T, I_P  =  2.5 MA. Figure 10 shows the comparison of the 16.4 MeV gamma-ray signal in JET discharge with D-NBI into the D–³He mixture described above, versus discharge with ³He minority ICRH in D plasma. The two green curves show the expected gamma-ray spectrum resulting from the de-excitation of two ⁵Li excited states, the ground one and the first excited state, both having a rather broad width. The energy of 16.4 MeV given in (9) is the mean gamma-ray energy corresponding to the de-excitation of only one of the excited states.

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In this series of discharges, fusion-born alpha particles were detected with the lost ion scintillator probe. Figure 11 shows an example of such measurements, with the somewhat lower energy of the alpha-particles caused by the alpha-particle slowing-down at the foil covering the entrance to the scintillator.

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This was a new technique of obtaining the D–³He fusion, which was expected to provide a higher efficiency of D–He³ yield per unit power as compared to the He³ minority ICRH in D plasma. The higher efficiency was expected due to the less extended tail of D ions accelerated with 3rd harmonic ICRH, which gives a cut-off at the energy of ~2 MeV, while the ³He-minority ICRH in D plasma generates a Stix type distribution with higher energy tail consuming ICRH power but not delivering much D–³He fusion. Furthermore, the 3rd harmonic ICRH provides an opportunity of controlling the cut-off D tail energy by changing plasma density, as explained in section 2.

The ICRH acceleration of D beams in D–³He plasmas was employed with amounts of ³He increasing discharge-by-discharge up to ${{n}_{\text{H}{{\text{e}}^{\text{3}}}}}/{{n}_{\text{e}}}\approx \text{3}0\%$. High resolution γ-spectrometry, NPA, scintillator probe, and Faraday cups were all employed for measuring ICRH-accelerated D ions and charged fusion products of both D–³He and D–D reactions. Alpha-particles born in D–³He fusion were seen best in the scintillator probe signal detecting lost ions just after NBI/ICRH switch off. Figure 12 compares the temporal evolution of the lost ion signal in the scintillator probe versus the D–D neutron rate. The measured loss decay time of ~0.04 s is approximately twice shorter than the decay time of D–D neutron rate, ~0.09 s. Taking into account that decay of the D–D neutron rate is determined by the slowing-down of fast D ions, and the slowing-down time of D ions, τ_SD ~ A/Z², is twice longer than that of alpha-particles, one concludes that the dominant contribution to the lost ion signal is not from the fast D ions, but from alpha-particles. Figure 13 shows the scintillator probe signal at the time of interest. One can see, indeed, that the peak losses have Larmor radius in excess of ~10 cm, in contrast to peak losses of fast ions with Larmor radius of ~6–8 cm in the experiments described.

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Details of other measurements are separately reported in [21], we only present here figure 14 summarising the D–³He fusion yield deduced from the 16.4 MeV gamma-ray measurements. Similarly to the fast ion D–D fusion described above, the relatively low electron temperature in JET with ILW caused a D–³He fusion rate lower than in both cases of D-NBI injection into D–³He plasma and ³He minority ICRH performed in JET with carbon wall.

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An interesting finding of this experiment was the observation of extremely long sawtooth-free periods in some of the discharges. A detailed study of this effect has been presented in [22].