Pulsed merging compression in a spherical tokamak reactor

Abstract

A method of operating a nuclear fusion device. The nuclear fusion device comprises a toroidal plasma chamber and has poloidal field coils configured to form a plasma within the plasma chamber by one of merging compression and double null merging. A varying current is provided to the poloidal field coils. The varying current comprises a plurality of pulses. Each pulse comprises a plasma formation period having a rate of change of current which is opposite in sign to the current; and a merging period following the plasma formation period and having a current sufficiently low in magnitude as to allow plasmas within the chamber to merge into a single plasma. The current during the plasma formation period is varied such that the energy density of the single plasma immediately after merging is sufficient for fusion to occur.

Claims

1. A method of operating a nuclear fusion device including a toroidal plasma chamber and having poloidal field coils configured to form a plasma within the plasma chamber by one of merging compression and double null merging, the method comprising: providing current to the poloidal field coils, the current is varied through applying a plurality of pulses, each pulse including: a plasma formation period where the sign of the current is opposite to its derivative; and a merging period following the plasma formation period, where the magnitude of the current is reduced to zero to allow plasmas within the chamber to merge into a single plasma, wherein the plasma formation period comprises a first plasma formation period with a positive current, and a second plasma formation period with a negative current.

2. The method according to claim 1, wherein the varying current is always greater than or equal to zero.

3. The method of generating neutrons, the method including operating a nuclear fusion device by a method according to claim 1.

4. The method according to claim 1 wherein the pulses are applied periodically.

5. The method according to claim 4, wherein a frequency of the pulses is greater than 1 Hz, more preferably greater than 10 Hz, more preferably greater than 100 Hz.

6. The method according to claim 4, wherein the varying current has half-wave symmetry.

7. The method according to claim 1, wherein a frequency of the pulses varies over time.

8. A method according to claim 7, and including, for each pulse: monitoring conditions within the plasma chamber or poloidal field coils following the merging period; initiating a subsequent pulse in dependence upon the monitored conditions.

9. A nuclear fusion device comprising: a toroidal plasma chamber; poloidal field coils configured to form a plasma within the plasma chamber by one of merging compression and double null merging; a controller configured to provide current to the poloidal field coils and to vary the current through applying a plurality of pulses, each pulse including: a plasma formation period where the sign of the current is opposite to its derivative; and a merging period following the plasma formation period where the magnitude of the current is reduced to zero to allow plasmas within the chamber to merge into a single plasma, wherein the plasma formation period comprises a first plasma formation period with a positive current, and a second plasma formation period with a negative current.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIGS. 1A to 1D are schematic illustrations of the stages of merging compression;

(2) FIG. 2 illustrates the principle of a “null point”;

(3) FIGS. 3A to 3D are schematic illustrations of the stages of double null merging;

(4) FIGS. 4A and 4B illustrate exemplary waveforms for pulsed merging.

DETAILED DESCRIPTION

(5) In the MAST experiment (a small spherical tokamak reactor), the relationship between the plasma thermal energy immediately following merging and the current and radius of the MC coils was found to be:

(6) $W_{\mathrm{th},\mathrm{tot}}={\left(\frac{R_c{I}_c}{100}\right)}^2-2\mathrm{and}{W}_{\mathrm{th},e}=0.25{\left(\frac{R_c{I}_c}{100}\right)}^2-2$

(7) Where R.sub.c, is the radius of each MC coil, I.sub.c is the peak current in each coil, W.sub.th,tot is the total thermal energy of the plasma and W.sub.the,e is the thermal energy of the electrons in the plasma. W.sub.th,i, the thermal energy of the ions in the plasma, is given by W.sub.th,tot—W.sub.th,e (neglecting impurities). There are other dependencies (e.g. on toroidal field strength, and potentially on the plasma volume), but considering only the dependence on the MC coil properties serves to illustrate the principle. In practice, this means that a high plasma thermal energy can be achieved with sufficiently high current—in particular, with sufficiently high current it is possible to achieve a sufficiently high ion thermal energy during merging to cause fusion without additional input. The resulting plasma would be transient and dissipate quickly unless measures were taken to maintain it, but fusion power and neutrons would still be generated for a short time.

(8) In current tokamak research, the focus has been on producing a stable plasma from MC and other means which can achieve sustained fusion. As an alternative, it would be possible to use MC alone to produce a short-lived “burning” plasma (i.e. one undergoing fusion). Once the burning plasma has been obtained it can be allowed to dissipate, without the need to maintain it for any length of time. Instead, the MC cycle can be repeated many times. A useful power output or a useful neutron flux can be obtained if the cycle is repeated several times per second.

(9) The fusion power per unit volume of a deuterium-tritium (D-T) plasma is given by P.sub.f=n.sub.Dn.sub.TσνE.sub.f, where E.sub.f is the energy per fusion (and is constant). For temperature T=10-20 keV, the velocity average reaction cross section σν is approximately proportional to T.sup.2. Taking n.sub.D=n.sub.T=n.sub.i/2 (i.e. equal quantities of deuterium and tritium), the fusion power per unit volume is given by:
P.sub.f∝n.sub.i.sup.2T.sup.2E.sub.f∝p.sub.i.sup.2E.sub.f
where p.sub.i=n.sub.iT is the thermal pressure of the ions in the plasma. This pressure is related to the thermal energy of the ions by

(10) $p_i=\frac{2}{3}\frac{W_{\mathrm{th},i}}{V}$
(where V is the volume of the plasma).

(11) Which gives:

(12) $P_f\propto {\left(\frac{w_{\mathrm{th},i}}{V}\right)}^2{E}_f\propto {\left(\frac{w_{\mathrm{th},i}}{V}\right)}^2\propto {\left(\frac{0.75{\left(\frac{R_c{I}_c}{100}\right)}^2-2}{V}\right)}^2$

(13) For P.sub.f in MW/m.sup.3, R in m, V in m.sup.3 and I in kA, the equation becomes:

(14) $P_f\approx 1.34\times 10^{-5}{\left(\frac{0.75{\left(\frac{R_c{I}_c}{100}\right)}^2-2}{V}\right)}^2$

(15) The total fusion power of the tokamak is given by P.sub.fV.

(16) The plasma volume V just after merging is approximately V≈2πR.sub.c×πa.sup.2, where a is the minor radius of the plasma torus.

(17) The volume dependence in the final equation may be the result of the as yet unknown volume dependence of the ion thermal energy density—i.e. there may be a volume dependence of the thermal energy density which means that there is no volume dependence of the fusion power density. In any case, this expression shows that once the plasma energy density after merging is sufficient for fusion, the resulting fusion power increases with the fourth power of the current in the MC coil—i.e. achieving higher energy output or neutron output is a matter of scaling up the MC coil current. For example, for a spherical tokamak with an MC coil radius of 0.75 m, and a plasma volume of 0.2 m.sup.3, a current of 1.7 MA would be required to give a 1 MW total power output.

(18) For double null merging, similar considerations will apply—though the relevant radius will be that of the null formed (as a general term to cover both MC and DNM, this can be referred to as the “radius of plasma formation”), and the dependency of the fusion power on the current of each coil will be more complicated. However, higher currents will still lead to higher fusion power once the plasma energy density on merging is sufficient for fusion to occur. Plasmas suitable for fusion other than D-T plasmas may be used, but are likely to require higher coil currents.

(19) FIGS. 4A and 4B show exemplary waveforms for a pulsed power merging source (with time and current in arbitrary units). Each current waveform 411, 421 is sinusoidal in this example, although it will be appreciated that any suitable waveform may be used.

(20) FIG. 4A illustrates a waveform 411 which oscillates around zero, and plasma formation will occur whenever the derivative of the current is the opposite sign to the current (i.e. on the downslope for I>0, and on the upslope for I<0, hereafter “plasma formation periods”). For this waveform three discrete periods of plasma current 412, 413, 414 are generated. The plasma currents 412 and 414 which are generated by the downslope of a positive coil current are positive, and the plasma current 413 which is generated by the upslope of a negative current is negative. Each cycle will have one plasma formation period with positive current, and one with negative current. In this idealised situation, the final plasma current is equal to the peak coil current. The starbursts 415, 416, 417 at the end of each plasma current plot show where merging of the plasmas from each coil occurs.

(21) FIG. 4B illustrates an alternative waveform 421 which is biased such that I≥0, with I=0 at each minimum. This may be provided by a combination of a variable (e.g. AC) source, and a DC source which provides a bias to ensure that the total current is greater than zero. The peak current of waveform 421 is therefore twice the peak current of the waveform 411 of FIG. 4A. Positive plasma currents 422, 423 are generated once each cycle in a plasma formation period on the downslope (i.e. where the derivative of the coil current is negative), with a merging event 424, 425 occurring when the coil current reaches zero. No negative plasma current can be generated, as any plasma formed during the upslope of the current would be repelled by the coil, the dotted line 426 shows the current which would be induced if such a plasma were possible.

(22) While the waveform 411 of FIG. 4A has twice as many plasma formation and merging events per cycle than the waveform 421 of FIG. 4B, the peak coil (and therefore plasma) current in FIG. 4A is about half that of FIG. 4B. As seen above, the fusion power scales with I.sup.4, so the fusion power per merging event with the waveform of FIG. 4B is as much as 16 times that of the waveform of FIG. 4A, resulting in a total average fusion power of about 8 times greater for the waveform of FIG. 4B compared to the waveform of FIG. 4A.

(23) The period of the waveforms will be primarily limited by the ability to generate high AC currents and the ability of the MC coils to withstand those currents. Typical MC waveforms have a period of about 10 ms, and it is expected that this could be replicated for a pulsed system, i.e. giving a frequency of 100 Hz (and therefore 200 plasma formation events per second for the waveform of FIG. 4A, or 100 plasma formation events per second for the waveform of FIG. 4B). Other frequencies of waveform may be used, e.g. greater than 10 Hz, greater than 20 Hz, or greater than 50 Hz. Waveforms other than sinusioidal waves may be used, e.g. a sawtooth wave or more complex forms. The waveform used may or may not include a compression phase—such a compression phase may increase the plasma energy, but significant fusion power will be generated purely from the merging.

(24) For waveforms such as those of FIG. 4A which include two plasma formation phases per cycle with opposite currents, the waveforms may be half-wave symmetric (i.e. when the waveform is shifted by half a period, the signal is the negative of the original signal) such that each of the two plasma formation phases per cycle is equal and opposite.

(25) It will be appreciated that the discussion above based on a sinusoidal waveform is intended to simplify explanation of the concept, and in practice alternative shapes of waveform may be used. In particular, it may be desirable to provide for periods between high current in order to allow recovery of the coils. It will also be appreciated that the applied current need not be strictly periodic, and as an alternative to using cycling waveforms, the plasma formation and merging periods may be provided as a series of individual pulses. The time between pulses may be variable, e.g. to provide a varying average neutron flux to a target. The pulses may be triggered by conditions within the reactor or coils as measured by a set of sensors, such as triggering a pulse when the previous plasma has dissipated or when coil deformation or temperature has recovered to an acceptable level.

(26) The reactor may comprise a coil cooling system configured to maintain the temperature of the MC/DNM coils.

(27) A device making use of the pulsed merging method described above may be used as a neutron source, or may be used for power generation. Such a device would comprise a toroidal plasma chamber and either merging compression coils within the plasma chamber, or double null merging coils located either inside or outside the plasma chamber (or with one coil of each pair located inside and the other located outside). Some source of helicity in the field (e.g. a toroidal field coil or a solenoid wrapped around the MC coils) will be required, but significantly less than would be needed for a conventional magnetic confinement fusion reactor, as there is no need to maintain the plasma for a significant length of time. This may reduce the requirements for toroidal field coils and other poloidal field coils compared to a conventional reactor, though their presence may allow further optimisations, e.g. pulsing other poloidal field coils in order to provide greater compression of the plasma after merging. In general, optimisations to improve plasma energy density on merging are beneficial. Optimisations which improve the stability of the plasma may be used if a longer duration of fusion in each pulse is desired.