Runaway electron losses caused by resonant magnetic perturbations in ITER

Transcription

1 Runaway electron losses caused by resonant magnetic perturbations in ITER G. Papp 1,2, M. Drevlak 3, T. Fülöp 1, P. Helander 3 and G. I. Pokol 2 1 Department of Applied Physics, Nuclear Engineering, Chalmers University of Technology and EuratomVR Association, SE41296 Göteborg, Sweden 2 Department of Nuclear Techniques, Budapest University of Technology and Economics, Association EURATOM, H1111 Budapest, Hungary 3 MaxPlanckInstitut für Plasmaphysik, Teilinstitut Greifswald, Germany papp@chalmers.se Abstract. Disruptions in large tokamaks can lead to the generation of a relativistic runaway electron beam that may cause serious damage to the first wall. To suppress the runaway beam the application of resonant magnetic perturbations (RMP) has been suggested. In this work we investigate the effect of resonant magnetic perturbations on the confinement of runaway electrons by simulating their drift orbits in magnetostatic perturbed fields and calculating the transport and orbit losses for various initial energies and different magnetic perturbation levels. In the simulations we model the ITER RMP configuration and solve the relativistic, gyroaveraged drift equations for the runaway electrons including a timedependent electric field, radiation losses and collisions. The results indicate that runaway electrons are rapidly lost from regions where the normalised perturbation amplitude δb/b is larger than 0.1% in a properly chosen perturbation geometry. This applies to the region outside the radius corresponding to the normalised toroidal flux ψ = 0.5. PACS numbers: Av, Dq, Fs, Ny, Fa Submitted to: PPCF

2 Runaway electron losses caused by resonant magnetic perturbations in ITER 2 1. Introduction The toroidal electric field generated due to the sudden cooling of the plasma in a disruption can give rise to an intense runaway electron beam. If these fast electrons hit the plasma facing components they can cause serious damage. Large tokamaks such as ITER could be more susceptible to the formation of runaway electron beams than present tokamaks. The reason for this is that the avalanche effect due to close Coulomb collisions with the background electrons becomes more significant for larger tokamaks with high currents. It can be shown that the ease with which runaways are generated increases exponentially with plasma current [1]. Due to avalanche multiplication, runaway currents of several megaamperes may be generated in an ITER disruption. The uncontrolled interaction of such a high energy electron beam with plasma facing components is unacceptable for nextstep devices and therefore the issue of how to avoid or mitigate the beam generation is of prime importance for ITER. Magnetic perturbations can be a possible way for runaway suppression [2]. Experiments of runaway suppression with externally generated perturbation fields have been conducted in several machines. In many cases it has been shown that magnetic perturbations could effectively suppress the runaway beam, e.g. in JT60U [3] and TEXTOR [4, 5, 6, 7]. But there are also examples where magnetic perturbations did not affect the runaway beam, e.g. in JET [8]. Previous simulations of the runaway electron drift orbits in a TEXTORlike configuration with resonant magnetic perturbations (RMP) have shown that the loss of highenergy runaways is dominated by the shrinkage of the confinement region, and is independent of the perturbation current [9]. The losses are mostly due to the wide orbits of the runaways that intersect the wall and therefore it is most effective for electrons close to the edge. The results indicated that the runaways in the core of the device are typically well confined; however, the onset time of runaway losses closer to the edge is dependent on the magnetic perturbation level and can affect the maximum runaway current. In larger tokamaks one may fear that magnetic perturbations would be less effective, simply because the runaways that are generated close to the centre will not come close to intersecting the edge stochastic region. However, in paper [9] it has been proposed that in connection with MHD perturbations caused by e.g. gas injection, core runaways could be transported towards the edge [10, 11]. Therefore edge magnetic perturbations together with gas injection could be an effective way of suppressing the runaway beam even in large tokamaks, such as ITER. An extrapolation of the effect of magnetic perturbations on runaway beam suppression from the existing experimental data to ITER is difficult, partly because the experimental results are not entirely understood, but also because runaway dynamics is expected to be different in ITER. The aim of the present work is to contribute to the understanding of runaway dynamics in perturbed magnetic field in an ITERlike scenario. This will be achieved by a threedimensional numerical modelling of the runaway electron

3 Runaway electron losses caused by resonant magnetic perturbations in ITER 3 drift orbits. We will present simulations of the runaway electron drift orbits in ITERlike perturbed magnetic fields and evaluate the effect of magnetic perturbations on runaway losses. In the simulations we use a timedependent electric field obtained for an ITERlike disruption scenario calculated with a model of the coupled dynamics of the evolution of the radial profile of the current density (including the runaways) and the resistive diffusion of the electric field [12]. We also include the effect of collisions along with synchrotron and Bremsstrahlung radiation losses. Previous studies on the ITER ELM perturbation system [13] aimed on ELM suppression during normal operation, where the deep penetration of the perturbation is undesirable. For the runaway mitigation, that is applied during a disruption, the aim is different. Deeper penetration, in principle, can lead to more efficient runaway suppression. In this article we study various perturbation current configurations based on the state of the art design of the ITER RMP coil system. The results indicate that runaway electrons can gain more than 100 MeV in an ITERlike disruption. They are rapidly lost from regions where the normalised perturbation amplitude δb/b is larger than This applies to the region outside the radius corresponding to the normalised toroidal flux ψ = 0.5. The losses are partly due to the confinement volume shrinkage for large energies and partly due to the fact that the stochasticity of the field lines leads to rapid radial transport. The numerically found threshold δb/b 10 3 confirms earlier analytical [2] and numerical [14] estimates for the perturbation level needed for runaway losses. The losses are sensitive to the chosen perturbation configuration. The paper is organised as follows: In Sec. 2 we give a description of the applied numerical model. In Sec. 3 the ITERlike scenario used in the simulations is described, including an estimate of the electric field. Also the structure of the magnetic field and the perturbation are described. In Sec. 4 the effect of RMP on the particles orbits is studied and the loss fractions of the runaway electrons are discussed. Furthermore, the effect of RMP and the toroidal electric field on the transport is described. Finally, the results are summarised in Sec Numerical model We solve the relativistic, gyroaveraged equations of motion for the runaway electrons including the effect of synchrotron and Bremsstrahlung radiation with the ANTS (plasma simulation with drift and collisions) code [9]. This code calculates the drift motion of particles in 3D fields and takes into account collisions with background (Maxwellian) particle distributions, using a fullf Monte Carlo approach. The collisions are modelled with a collision operator that is valid for both nonrelativistic and relativistic energies. The magnetic field is defined on a mesh in the entire domain of computation, and the integration of the particle orbits is carried out in Cartesian coordinates. This approach

4 Runaway electron losses caused by resonant magnetic perturbations in ITER 4 provides the greatest flexibility and facilitates a faithful treatment of magnetic fields with islands and ergodic zones, since the existence of magnetic surfaces is not required. In the case of electrons with some hundred MeV energy the radiation losses cannot be neglected. Therefore synchrotron radiation and Bremsstrahlung losses are included in the simulations. Synchrotron radiation is included in the form derived in the Appendix of our previous work [9]. The term arising from the guiding centre motion associated with the major radius R = 6.2 m is neglected, because even at very large energies the Larmor motion dominates the radiation for the ITER parameters, as shown in figure Ratio of toroidal / larmor component of synch. rad Toroidal / Larmor ITER Energy (MeV) Figure 1. Comparison of the guiding centre term and the Larmor term in the synchrotron radiation for the ITER parameters. The guiding centre term is at least an order of magnitude smaller even at very high (> 200 MeV) energies. Bremsstrahlung radiation is included in the form of a decelerating force, dp/dt = F B, dp /dt = F B p /p [15], where F B = 4 ( 137 m ec 2 ren 2 e (Z eff 1)γ log 2γ 1 ), (1) 3 m e is the electron rest mass, c the speed of light, r e the classical electron radius, n e the plasma electron density, Z eff the effective charge and γ is the relativistic gamma factor for the particle. It follows from the above that dp /dt = F B p /p. 3. ITER scenario The simulations have been carried out for the ITER scenario #2 (15 MA inductive burn) [16]. Inductive scenarios are expected to produce the largest and most energetic populations of runaway electrons. We investigate pure disruptions without impurity injection disruption mitigation. We use a postdisruption equilibrium with the parameters shown in table 1 and figure 2, based on simulations with the ASTRA code [16, 17]. The core plasma temperature was set to the estimated 10 ev postdisruption value [18].

5 Runaway electron losses caused by resonant magnetic perturbations in ITER 5 Table 1. The plasma parameters used in the simulations. Parameter name Notation Value Major radius R m Minor radius a 2 m Magnetic field on axis B 5.26 T Effective charge Z eff 1.6 Normalised flux ψ Ψ(r)/Ψ(a) Normalised radius r/a r/a ψ Plasma current I p 15 MA Density on axis n m 3 Predisruption temperature on axis T pre kev Postdisruption temperature on axis T post 0 10 ev Approx. temperature profile T e (ψ) T 0 (1 0.98ψ) q on axis q q on edge q a 3.8 q profile q(ψ) q 0 ( 1 [1 (q0 /q a ) 1/α ] ψ 2) α, α = 2.09 Density [10 19 /m 3 ] ITER SCEN #2 15MA IND. (ASTRA) (a) Electron density Ion density Radial position (normalized flux) Temperature [ev] (b) ITER SCEN #2 15MA IND. 10 ev (ASTRA) Electron temperature Ion temperature Radial position (normalized flux) Figure 2. (a) Density and (b) temperature profiles for the electrons and ions as used in the simulation Energy gain due to the electric field The maximum energy E that a runaway electron can gain in a tokamak disruption is limited by E ecδψ/r, where δψ is the change in the poloidal flux caused by the decay of the plasma current. For large aspect ratio and circular cross section we have dψ/dr = rb/q(r), so on the axis (where the drop in ψ is the largest) δψ B a r/q(r)dr 0 Ba2 /3 for a typical ITER inductive burn scenario qprofile. Thus the absolute upper limit of the reachable energy is E eca 2 B/3R 340 MeV for the simulation parameters (B 0 = 5.3 T, a = 2 m, R = 6.2 m). This is significantly larger than the 20 MeV estimate on smaller devices [9]. The selfconsistent computation of the accelerating electric field during runaway generation is nontrivial [19, 20]. For this work we used a timedependent electric field (shown in figure 3) which is taken from simulations of the evolution of the radial profile

6 Runaway electron losses caused by resonant magnetic perturbations in ITER 6 of the current density and the diffusion of the electric field [12]. In figure 3b the energy gain of the particles up to t = 45 ms is shown, calculated as E(t) = e t v(τ) E(τ)dτ 0 ec t E 0 φ(τ)dτ. From this figure it is clear that particles can reach energies in excess of 100 MeV in an ITER disruption. Due to the nonmonotonic initial current profile [16], the most energetic runaways are expected around midradius. Note that 100 MeV is the maximum energy reachable by electrons. Once the avalanche starts, the electron distribution will be dominated by lower (in the order of 10 MeV) energy particles. Figure 3. (a) Temporal and radial evolution of the toroidal electric field E φ. (b) Energy gain of the particles due to the electric field as a function of time and radius Magnetic field structure and perturbations The unperturbed magnetic equilibrium has been calculated by VMEC [21] for the parameters above and the ITER scenario #2 PET separatrix [16]. The equilibrium used in the simulations is presented in figure 4a along with the crosssection view of the ITER RMP coils on the low field side of the plasma. As in previous work [9], we neglect the effect of shielding of magnetic field perturbations by plasma response currents. This approximation is expected to be valid in cold postdisruption plasmas, and indeed, in smaller tokamaks such as TEXTOR it was shown that RMP could effectively increase the radial transport of runaways, which it would not have been able to do if it the perturbation had been shielded out from the outer regions (ψ 0.5). Clearly, if the effect of shielding were included, it would reduce the perturbations and therefore also the runaway losses. Thus our results should be interpreted as an upper limit on the actual losses. The perturbed magnetic field is obtained by superimposing the field from the perturbation coils on the field of the unperturbed VMEC solution. This approximation is valid because the field generated by the perturbation coils is much smaller than that from the toroidal field coils and the plasma current.

7 Runaway electron losses caused by resonant magnetic perturbations in ITER 7 Z [m] (a) R [m] (b) Figure 4. (a) Crosssection view of the VMEC equilibrium (green) and the PET equilibrium separatrix (red). The RMP coils are marked with blue lines. (b) 3D Sketch of the ELM perturbation coil configuration as implemented in the simulation. The runaway electron drift orbits have been calculated for the 15 MA inductive scenario using the ELM perturbation coils as the source of RMP. The ELM perturbation coilset consists of 9 3 quasirectangular coils at the low field side of the device, shown in figure 4b. Electrical currents flowing in these coils generate a perturbation field, and a sufficiently large perturbation results in an ergodization of the magnetic field lines. These coils create magnetic perturbations at the plasma periphery on the low field side of the torus that decay radially toward the inside of the plasma * sqrt[<(db/b) 2 >] (a) 0.1% ITER RMP: 60 ka n=3 (all) n=9 midreversed n=9 basic Radial position (normalized flux) Basic (b) Midreversed ( R ) Figure 5. (a) Radial dependence of the flux surface average (δb/b) 2 for I RMP = 60 ka in n = 9 and n = 3 operational modes. (b) Sketches of the 1/9 part view of the basic n = 9 and midreversed ( R ) n = 9 RMP configurations. The radial variation of the fluxsurface averaged magnetic perturbation level

8 Runaway electron losses caused by resonant magnetic perturbations in ITER 8 (δb/b)2 for I pert = 60 ka is shown on figure 5a. For other perturbation amplitudes the values can be calculated from (δb/b) 2 I pert. The magnetic perturbation level that is predicted to be necessary for runaway suppression is δb/b 10 3 [2, 14]. The technically achievable upper limit of 60 ka can generate such a perturbation level up to the fluxsurface ψ = , while having δb/b = 10 3 in the centre would require I pert 180 ka. Since the ITER RMP consists of 9 3 coils, the natural configurations have n = 9 or n = 3 lead toroidal modenumber. The two ways to operate the coils in the n = 9 case is to either have the same current direction in all the coils (basic) or to reverse the current direction on the midplane (midreversed or R ) as shown in figure 5b. In the basic configuration the toroidal currents at the midplane more or less cancel out, that leads to smaller perturbation level, as shown in figure 5a. The different n = 3 configurations that will be shown later are constructed to have the same relative perturbation as the n = 9 R configuration (see figure 5a). A Poincaré plot of the magnetic flux surfaces in the n = 9 perturbed and nonperturbed equilibrium are shown in figure 6. We did not apply any mapping technique. The field lines are directly integrated in Cartesian coordinates similar to the particles for the same reasons as described before. For better visibility, the Poincaré plots obtained in the (R, Z) plane are converted to flux coordinates (θ, ψ). An approximation for these coordinates was obtained by extracting the radial coordinate from the unperturbed VMEC equilibrium and using θ = atan2(z, R). The determination of the exact flux coordinates in perturbed fields is complicated and is outside he scope of the present paper. As expected, the edge region becomes distorted as a result of the RMP. As the magnetic perturbation grows, magnetic islands appear, the locations of which are correlated with rational values of the safety factor. At n = 9 these islands are very small and have high poloidal modenumber, therefore there is no significant overlapping or broad ergodic zone generation. Figure 6. Poincaré plot of the magnetic field lines in the (a) unperturbed case and (b) in the n = 9 midreversed configuration for I pert = 60 ka. No significant ergodization of the edge region.

9 Runaway electron losses caused by resonant magnetic perturbations in ITER 9 Figure 7. Sketches of the 120 view of the four different n = 3 configurations (A D from left to right). Islands created by lower modenumber perturbations are considerably larger. The four possible n = 3 configurations (shown in figure 7) have equal relative perturbation that is almost the same as in the n = 9 configuration (figure 5) but can create much larger islands and ergodic zones. Figure 8. Poincaré plot of the magnetic field lines in four different n = 3 configurations for I pert = 60 ka. Interestingly, the various n = 3 configurations give rise to quite different magnetic

10 Runaway electron losses caused by resonant magnetic perturbations in ITER 10 structure and that in turn will give rise to different loss rates. Poincaré plots of the four different n = 3 configurations are shown in figure 8. Configurations A and B create broad ergodic zones at the plasma periphery, while C and D generates a series of nonoverlapping islands that are expected to keep the particles confined for longer time than in the other two cases. 4. Runaway losses 4.1. Confinement volume shrinkage The drift topology for high energy particles can significantly differ from the magnetic topology in both perturbed and unperturbed magnetic fields [22, 23]. For this reason we begin by showing Poincaré plots of particle orbits. The plots were converted from (R, Z) to (θ, ψ) coordinates the same way as the magnetic field lines, and the particles are shown in the magnetic and not the drift coordinate system. One particle was launched at each radial position and was followed for t = 100 µs simulation time. We illustrate the structure of the perturbation and the shrinkage of the confinement volume for various configurations and particle energies. Even in the unperturbed case, the confinement volume shrinks and the particle population is shifted towards the Low Field Side (LFS) with increasing energy, see figure 9. Figure 9. Poincaré plot of the particles at I pert = 0 ka (a) 10 MeV (b) 100 MeV (c) 200 MeV. Figure 10 shows the Poincaré plots of 10 MeV particles in the four n = 3 configurations with perturbation current I pert = 60 ka. Clearly, the edge region becomes ergodic and particles in this region are expected to be lost rapidly. In the case of C edge islands confine the particles.

11 Runaway electron losses caused by resonant magnetic perturbations in ITER 11 Figure 10. Poincaré plot of 10 MeV particles at I pert = 60 ka for the four n = 3 configurations. The confinement volume shrinkage due to increasing particle energies and the RMP is illustrated in figure 11 for two different particle energies. Here we switched off energy modification terms (electric field, collisions, radiation) to study the behaviour of monoenergetic particle species and to explore the confinement shrinkage phenomenon as a function of particle energy. The particles were followed only up to 1 ms, during which they would not gain or lose too much energy in any way (see figure 3b). Particles were launched equidistantly in r/a (and not in normalisedflux), hence the loss percentage stands for shrinkage measured in r/a, not as the exact shrinkage of the confinement volume itself. Since r/a ψ, the shrinkage of the confinement volume can be expressed as y 2 = 1 (1 y 1 ) 2 where y 1 denotes the losses shown on the left hand side vertical axis of the loss figures 11ab. The confinement volume shrinkage is shown on the right hand side axis (y 2 ). The position of the last confined flux surface in the flux coordinate (ψ) can be expressed as (1 y 1 ) 2. Hence for a 25% particle loss on the figure the Last Closed Flux Surface (LCFS) is ψ = 0.56, and the confinement volume shrinkage is 44 %. As expected, at lower energies (10 MeV, figure 11a) the particles are mostly confined in the unperturbed case and in the cases C and D. In the other perturbed

12 Runaway electron losses caused by resonant magnetic perturbations in ITER 12 % of particles lost n=3 "A" n=3 "B" n=3 "C" n=3 "D" UNPERT. E tor = 0 V/m E init = 10 MeV I RMP = 60 ka (a) time [us] % of conf. V. shrinkage % of particles lost n=3 "A" n=3 "B" n=3 "C" n=3 "D" UNPERT. E tor = 0 V/m E init = 100 MeV I RMP = 60 ka (b) time [us] Figure 11. Confinement volume shrinkage for the four different n = 3 perturbations at (a) 10 MeV and (b) 100 MeV particles. The largest and fastest shrinkage is caused by the D configuration. % of conf. V. shrinkage cases they are less confined, depending on the chosen magnetic configuration, although the configurations were constructed so that the normalised magnetic perturbation amplitudes are the same. The most efficient of the four cases from figure 8 is case B, and therefore in the following we will study the losses caused by this perturbation configuration. Figure 11b shows the fraction of lost 100 MeV particles. This energy is close to the maximum achievable during the disruption, which will not be reached by many particles. As expected, even the unperturbed case will lead to particle losses, that is a clear indication of the confinement volume shrinkage due to the increased particle energy. The new LCFS for the 100 MeV particles will be around the original ψ 0.5 surface ( 50% confinement volume shrinkage). The different configurations converge to the unperturbed case: with increasing energy the effectiveness of the RMP drops, but the particles outside the new LCFS associated with their energy are lost anyway due to their increasing energy. Since the time axis is logarithmic, the A and B configurations are preferable to C and D, because they cause losses orders of magnitude faster than the latter ones. Rapid losses are beneficial because that makes the avalanche generation less effective. Furthermore, the faster the particles are lost the less energy they can obtain from the electric field Runaway losses In the unperturbed case, the particles that reach the edge of the confinement volume will get lost. The confinement volume shrinks with increasing particle energy. Since the particles can gain a significant amount of energy (up to 100MeV) during the disruption, roughly the outer 4050% of the confinement volume will be lost (see figure 11b) and the new LCFS will be around the original ψ 0.5. For this reason there is no significant difference in the losses if we launch particles with 10 kev, 100 kev or 1 MeV: the difference in the starting energy is almost negligible compared to the energy gain. Losses start roughly 1 ms sooner in the 10 MeV unperturbed case as compared to 1 MeV, but the

13 Runaway electron losses caused by resonant magnetic perturbations in ITER 13 loss dynamics is the same. Launching particles with even higher energy is unrealistic, because only a negligible amount of such energy particles is expected before the disruption. Therefore from now on we will present particles with 1 MeV initial energy. Increasing the effective charge of the plasma an order of magnitude does not make any significant difference in the loss dynamics. The same stands for the Bremsstrahlung and synchrotron radiation losses, these two effects do not have significant influence on the loss dynamics. If we launch the particles on a flux surface that is within the confinement zone but will be outside it at large energies e.g. ψ = 0.7, we will observe particle losses even without perturbation. This is caused solely by the high energy that the particles reach during he disruption. The fraction of lost particles in the unperturbed case is shown in figure 12a. The particle is lost if its energy reaches the critical energy that is required for its actual position to be outside the LCFS associated with that energy. Launching particles within the ψ 0.5 limit will cause no particle losses, as confirmed by direct particle simulations. % of particles lost ψ = 0.7 E tor (t) E init = 1 MeV I RMP = 0 ka (a) UNPERT 1 MeV time [ms] % of particles lost (b) E tor (t) E init = 1 MeV n=3 'B', 60kA ψ=0.7 ψ=0.6 ψ=0.5 Log(t) fit time [ms] Figure 12. Particle losses (a) without and (b) with perturbation. In the perturbed case the ergodic zone arising at the edge will cause losses several orders of magnitude faster than in the unperturbed case. As shown on figure 12b, particles launched at ψ = 0.7 start to get lost already after 1 µs, and losses continue with logarithmic temperature dependence until 0.1 ms (note the logarithmic time axis on the figure). At around 0.1 ms already 95% of the particles are lost, but the remaining 5% takes up to 3 ms to get lost. Similar dynamics is observable if the particles are launched at the fluxsurface ψ = 0.6. The particle losses start an order of magnitude later at 10 µs, and dynamics of the losses is the same: logarithmic losses up to 0.2 ms, where around 95% of the particles are lost, followed by a longer period during what the remaining particles are also lost within 10 ms. If we go one more ψ = 0.1 step further in, the losses start again 10 times later at 100 µs, and the logarithmic dependence will be the same. In this case not all the particles will be lost, since the high energy LCFS is in the vicinity of the ψ = 0.5 surface. Particles launched further in, e.g. at ψ 0.5 will not get lost even with strong RMP. The swift onset followed by logarithmic losses is a clear result of the RMP, although it seems to be less effective after a given amount of time. This is due to the fact that

14 Runaway electron losses caused by resonant magnetic perturbations in ITER 14 particles launched at a certain fluxsurface get an instant spread dictated by the drift orbit width. Also those particles that initially drift inwards will be transported outwards eventually, but it takes longer for them to get lost. The logarithmic loss dynamics show that most of the particles are lost during the early phases of the losses, which seems to be favourable from the avalanche generation point of view. Also, the particles lost due to RMP will have low energy (see figure 3b), while the losses caused by the shrinkage of the confinement zone result in lost particles in the 100 MeV energy range. Thus, RMP not only increases the amount of the particles lost outside ψ=0.5, it might also significantly weaken the avalanche generation in that region and results in lost particles at several orders of magnitude lower energies. Increased losses at the edge can also help to prevent a runaway electron sheet formation close to the boundary in the case of vertical displacement events (VDE) [24]. All of these results are beneficial from the runaway electron suppression point of view. However, losing fast electrons from the edge may lead to a larger inductive field in the centre of the plasma, making the avalanche stronger there. Therefore, quantitative conclusions about the magnitude of the total runaway current can only be drawn from simulations where both the evolution of the electric field and losses due to RMP are included selfconsistently. % of particles lost E init = 1 MeV I RMP = 60kA ψ = 0.7 E tor (t) n=3 "A" n=3 "B" n=3 "C" n=3 "D" n=9 "R" time [ms] Figure 13. Particle losses in the four different n = 3 and in the n = 9 midreversed configuration, I pert = 60 ka in each case. Initial launch surface is ψ = 0.7. As was already shown in figures 6, 8, 10 and 11, the perturbation geometry plays an important role in the behaviour of the magnetic structure and the losses, even though the relative perturbation magnitude is the same (figure 5a). This was also confirmed by direct particle simulations as shown in figure 13. As was postulated before, the B configuration causes the strongest losses, followed by A. C is roughly an order of magnitude less effective, while D and the stronger midreversed n = 9 configuration causes just a slight increase in the particle losses as compared to the unperturbed case. In the n = 9 case, the first losses occur after 10 ms, as a result of the inevitable confinement volume shrinkage with increasing energy. This result shows that a careful choice of the perturbation configuration (the current distribution in the 9 3 coils) is

15 Runaway electron losses caused by resonant magnetic perturbations in ITER 15 extremely important for the runaway suppression. tested configurations. Option B is the best out of the The statistical significance of the simulations can be improved by increasing the number of particles. The standard deviation can be estimated with σ(n) N that is for 100 particles 0 < σ < 10. We have verified the results presented in this paper by increasing the number of launched particles in a few test cases with up to a factor of 10. Our results show that there is no significant difference between the results with 100 and 1000 particles. Increasing the number of test particles does not influence the start or endpoints, nor the slope of the loss rate curves. 5. Conclusions In this paper we have studied the effect of magnetic perturbations on runaway electrons in ITER. The calculations were done for the ITER inductive scenario #2 [16, 17] and the simulations were performed with the ANTS code [9], taking into account synchrotron and Bremsstrahlung radiation losses and collisions. In the simulations we used a timedependent electric field calculated with a code that solves the coupled dynamics of the evolution of the radial profile of the current density (including the runaways) and the diffusion of the electric field [12]. As expected, we found that runaways in the core (ψ 0.5) are well confined, since the normalised magnetic perturbation is not strong enough there. However, runaways are rapidly lost if δb/b 10 3, which corresponds to the region outside the normalised flux ψ = 0.5. The losses are caused partly by the confinement volume shrinkage that the highenergy electrons experience as they are accelerated by the electric field [9, 22], and partly by the increased radial transport in the stochastic region. We performed simulations for several perturbation configurations and concluded that runaway losses are quite sensitive to the perturbation configuration. We identified one of the possible n = 3 perturbations to be the most efficient in this respect. The results indicate that the presence of RMP not only increases the amount of lost particles but may also counteract the avalanche generation at the edge, since it leads to earlier losses of particles with lower energies. However, the runaway losses are sensitive to the evolution of the electric field, thus the effect of the RMP on the whole runaway electron population and dynamics can only be estimated with more complex simulations that take into account the electric field dynamics selfconsistently. This could be achieved e.g. by the ARENA code [19], using the results presented in this paper as inputs, possibly in a form of radial transport coefficients and/or timedependent losses at the edge. Runaway electron diffusion may also be affected by microscale magnetic turbulence, which can be large in disruptive plasmas. However, Ref. [25] showed that their diffusivity scales inversely with the energy E 1 for magnetic transport or even with E 2 in case finite gyroradius effects become important. Therefore runaway electrons are usually well confined in disruptive plasmas, as was observed in JET disruption experiments, unless measures are taken to increase their radial transport.

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