Plasma steering to avoid disruptions in ITER and tokamak power plants
PPlasma steering in ITER to avoid disruptions
Allen H Boozer
Columbia University, New York, NY [email protected] (Dated: February 4, 2021)Steering ITER plasmas is commonly viewed as a way to avoid disruptions and runaway electrons.Plasma steering sounds as safe as driving to work but will be shown to more closely resemble drivingat high speed through a dense fog on an icy road. The long time required to terminate an ITERdischarge compared to time over which dangers can be foreseen is analogous to driving in a dense fog.The difficulty of regaining plasma control if it is lost resembles driving on an icy road. Disruptionsand runaways are associated with three issues—a solution to one tends to complicate the solutionto the other two: loss of plasma position control, excessive heat deposition, and wall melting due torunaway electrons. All three risks must be addressed for ITER to achieve its mission and essentiallyeliminated before tokamak power plants can be deployed.
The tokamak literature asserts that disruptionsand runaways are a problem of plasma steering. Thiscan be found in a
Physics Today article [1], whichsays the production of fusion energy will be enabledby the questions that ITER will answer, and in a
Nuclear Fusion article [2] reviewing progress on dis-ruption prevention for ITER.The purpose of this paper is to clarify issues ofplasma steering that need to be addressed for ITERto achieve its mission and for tokamak fusion-energyto be practical. Even problems that were consideredsolved, such as plasma-position control when sur-rounded by a perfectly conducting chamber [3–5],can be more subtle than was thought.The steering of tokamaks to avoid disruptions isanalogous to steering a car to avoid accidents. Steer-ing, whether a car or a tokamak, has two fundamen-tal problems.The first problem for steering is foreseeing dan-gers. To safely steer a car in foggy conditions,the speed of the car must be limited so it can besafely stopped within the distance at which danger-ous conditions can be foreseen. The tokamak ana-logue would be to limit the plasma current to a levelat which it can be terminated without a disruptionwithin the time danger can be foreseen.A review of ITER shutdown strategies [6] foundthat even under ideal conditions at least 60 s is re-quired to terminate a 15 MA ITER current withouta disruption. Predictions of disruptions during theflattop period of DIII-D plasmas [7] show a precipi-tous drop in reliability after milliseconds, Figure 1,but even the short-time predictions had only mod-est reliability, approximately 95%. Even one in tenthousand pulses ending in an unmitigated disrup-tion could have a large impact on the achievementof the ITER mission [2]. The problem of disruptionprediction is both challenging and important. A fewof the many recent references are [8–11]. Steeringa tokamak to avoid disruptions resembles driving a
FIG. 1: The fraction of DIII-D disruptions that weresuccessfully predicted versus the prediction time is illus-trated. F1 and F2 are two different weightings of thedata. This figure is reproduced with permission fromNucl. Fusion car at high speed through a dense fog.The tokamak literature recognizes and discussesemergency shutdowns [2, 12] that must be initiatedorders of magnitude faster, ∼
30 ms. This requires ahighly reliable strategy for instigating a benign dis-ruption, called disruption mitigation. But, as notedin 2019, “
With ITER construction in progress, reli-able means of RE (runaway electron) mitigation areyet to be developed ” [13]. Fast shutdowns can alsoproduce unacceptable forces on the blanket modulesin ITER. Subtleties in estimating these forces arediscussed in [14].The second problem for steering is the availabil-ity and timescale of actuators, the analogs of thesteering wheel and the brake pedal of a car and the1.5 s response time of a typical driver. For ITERthe actuators are (1) the external loop voltage, (2) a r X i v : . [ phy s i c s . p l a s m - ph ] F e b he externally produced axisymmetric poloidal mag-netic field, (3) particle injection systems, (4) parti-cle pumps, (5) heating and current drive systems,(6) non-axisymmetric external magnetic fields. Themajor papers on plasma steering do not discuss theprecise use of these six actuators, even in an un-rushed shutdown [6]. Indeed, it is unclear how to usethe actuators to control what are most important foravoiding disruptions: the profile of the plasma cur-rent, the loss of position control of the plasma, andthe maintenance of a sufficient plasma temperatureto avoid runaways. All of the ITER actuators exceptparticle injection require a timescale of order sec-onds to be fully effective, which is too long to reactto a number of envisioned situations, which requirea shutdown in of order tens of milliseconds [2, 12].Even when dangers can be adequately foreseen, in-tegration is required between the predictors and theactuators for successful steering. Once plasma con-trol is lost on ITER, it is difficult to regain, muchlike driving on an icy road.Why does it take so long to shutdown an ITERplasma? Magnetic fields produced outside the vac-uum vessel require 0.6 s to penetrate to the plasma[15], and voltage limits on the poloidal field coilstypically limit large changes to times longer thanseveral seconds [6]. The toroidal loop voltage on thevessel [15] must be less than 12 V. At 15 MA, thepoloidal magnetic flux enclosed by the ITER vacuumvessel can reach 75 V · s, so more than 6 s would berequired to remove it using the loop voltage on thevessel. The poloidal flux removal by the resistivityof a 10 keV plasma at the magnetic axis in ITERrequires ∼ (cid:96) i is a measure. The larger (cid:96) i , themore centrally peaked the current and the greaterthe tendency of the plasma to disrupt, Figure 2, andthe more difficult it is to keep the plasma adequatelycentered in the chamber [6]. As the plasma currentdrops, the plasma density must be proportionatelyreduced to stay below the empirical Greenwald den-sity limit [16], and this requires not only particletransport out of the plasma but also particle removalfrom the plasma chamber.The difficulty of benignly shutting down ITER be-comes far greater during its nuclear phase than be-fore. Control over the power input is lost, and farmore dangerous seeds for the transfer of the plasmacurrent from thermal into relativistic electrons arepresent. Even before the shutdown, steering be-comes more difficult in a nuclear-powered plasma.The current-density profile was identified in [2] asthe main drive for disruptive instabilities, but whichactuators ensure careful control of that profile over FIG. 2: The probability of disruption versus the inter-nal inductance (cid:96) i during DIII-D flattop periods. Thisfigure is reproduced with permission from Nucl. Fusion timescales long compared to internal flux relaxationtimes in a burning-plasma? The issue may beavoided in ITER by limiting the time a plasma maybe allowed to burn, but what is the solution in apower plant?For success in a disruption-free shutdown of aburning plasma, the reduction in the plasma pres-sure must be consistent with adjustments to the ex-ternal vertical field for the plasma to remain suffi-ciently centered in the machine to avoid wall contact.Loss of centering resembles going into a skid on anicy road; regaining centering can easily become im-possible. The speed of these adjustments is strictlylimited by the allowed voltages on the superconduct-ing poloidal field coils [6]. This is more difficultwhen deuterium-tritium fusion contributes 500 MW,of which 100 MW heats the plasma, with 50 MW ofavailable external power. The fusion power P dt isproportional to the plasma pressure squared within10% accuracy between 10 and 20 keV [17]. Withouta large increase in the poloidal-beta as the plasmacurrent I p is reduced, P dt drops as I p . The effecton the plasma pressure of the precipitous drop innuclear power as I p is decreased is magnified if theplasma switches from the high confinement H-modeto the low confinement L-mode [2].A reduction in the plasma current by a megaam-pere amplifies the number of energetic electrons bya factor of ten in a hydrogenic plasma [18]—evenmore when impurities are present [19, 20]. In thepre-nuclear phase of ITER, the only electrons thatare energetic enough to runaway are those that werein a high- T e Maxwellian tail before the electron tem-perature T e was reduced sufficiently for the resis-tive electric field ηj || to exceed the Connor-Hastieelectric field [21]. This is when runaway becomespossible, and at the standard ITER density requires2 e < ∼
550 eV. The change from a high electron tem-perature T e ∼
10 keV to a low temperature mustoccur quickly, in less than the maximum collisionalrelaxation time of an energetic electron, the Connor-Hastie [21] collision time τ ch ≈
20 ms. In the nuclearphase of ITER operations, two important steadysources of energetic electrons are available: tritiumdecay and Compton scattering by gamma-rays fromthe irradiated wall, which can be amplified into dan-gerous relativistic-electron currents [22].The seriousness of a disruptions and runaways isdetermined not only by the damage but also by thelength of the shutdown required for repairs. Thisis much longer after D-T operations in ITER begin.Issues associated with ITER maintenance and repairwere reviewed in 2019 by van Houtte [23].Disruptions and runaways are associated withthree issues—a solution to one tends to complicatethe solution to the other two: loss of plasma positioncontrol, excessive heat deposition, and wall meltingdue to runaway electrons. All three risks must be re-tired before tokamak power plants can be deployed.Even the successful achievement of the ITER mis-sion will require not only the avoidance of disrup-tions in the narrow sense of a sudden loss of magneticsurfaces but also the avoidance of the production ofmulti-megaamperes of relativistic electrons. Unac-ceptable melting [13] can be produced by 1.9 MA ofrelativistic electrons striking the walls over a broadarea, or 300 kA if concentrated. The risks of disrup-tions and runaway electrons are related but shouldnot be conflated [14]. In particular, the avoidance ofmagnetic-surface breakup can exacerbate the risk ofrunaway electrons.Fusion has the potential of making a major con-tribution to stopping the increase in atmosphericcarbon dioxide [24]. For this, minimization of timeand risk for a demonstration fusion power plant isof greatest importance. The cost of each year’s de-lay in developing a solution, of order a trillion dol-lars, far exceeds the credible cost of a minimal timeand risk program. The cost of deploying a sufficientnumber of fusion reactors to have a significant effecton carbon dioxide production is order a thousandtimes greater than constructing a demonstration fu-sion power plant. Nevertheless, having one workingfusion power plant is important in itself to worldsecurity. The precise cost of fusion energy is onlyrelevant during the deployment phase in compari-son with other solutions—and each of the alterna-tives for a complete energy system has major disad-vantages in comparison to fusion [24]. The cost ofelectricity and the minimum unit size are only twoconsiderations. Others can be more important: in-termittency, site specificity, waste handling, and the potential for nuclear proliferation.Making the risks of disruptions and runaways ac-ceptable in ITER is difficult but far easier thanin DEMO, a machine that can demonstrate fusionpower [25]. The basic problem is the structures sur-rounding the plasma are more delicate in a powerplant than they are in ITER. In addition, the diag-nostics, which are needed for steering, become muchmore limited [26].Many believe prudence requires a focus forDEMO on ITER-like plasmas because of their largerdatabase. However, magnetic fusion systems canbe designed to be robust against disruptions andrunaways by making them non-axisymmetric. Non-axisymmetry has additional advantages [24]: (1) fastand low-cost computational design that is far morereliable than in other fusion concepts because theplasma can be externally controlled, (2) an order ofmagnitude more parameters that can be used for op-timization, (3) divertor solutions far less restrictedby density limits [16], and (4) and even the potentialfor coils consistent with open access to the plasma.Disruption and runaway issues are far more chal-lenging in a tokamak power plant than during D-Toperations of ITER and far more challenging in D-Toperations of ITER than in non-D-T operations. Ademonstration that disruption and runaway issuescan be adequately addressed for practical tokamakfusion power will have to wait approximately thirtyyears until this can be demonstrated by power plantshaving operated an adequate period of time. A neg-ative conclusion on practicality could come sooner:after fifteen years when D-T operations start onITER or after five years when ITER starts plasmaoperations.Careful thought is required to determine howtimescales should be integrated within an overall fu-sion program designed to minimize risk and time indemonstrating fusion power at the level required forinformed decisions on its deployment. Each year’sdelay in deploying carbon-free energy systems notonly costs of order a trillion dollars [24] but also af-fects security worldwide.
Acknowledgements
This material is based upon work supported bythe U.S. Department of Energy, Office of Science,Office of Fusion Energy Sciences under Award Num-bers DE-FG02-03ER54696, DE-SC0018424, andDE-SC0019479.3
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