Jari Varje

Monte Carlo method and High Performance Computing for solving Fokker-Planck equation of minority plasma particles

This paper explains how to obtain the distribution function of minority ions in tokamak plasmas using the Monte Carlo method. Since the emphasis is on energetic ions, the guiding-center transformation is outlined, including also the transformation of the collision operator. Even within the guiding-center formalism, the fast particle simulations can still be very CPU intensive and, therefore, we introduce the reader also to the world of high-performance computing. The paper is concluded with a few examples where the presented method has been applied.

ITER fast ion confinement in the presence of the European test blanket module

This paper addresses the confinement of thermonuclear alpha particles and neutral beam injected deuterons in the 15 MA Q = 10 inductive scenario in the presence of the magnetic perturbation caused by the helium cooled pebble bed test blanket module using the vacuum approximation. Both the flat top phase and plasma ramp-up are studied. The transport of fast ions is calculated using the Monte Carlo guiding center orbit-following code ASCOT. A detailed three-dimensional wall, derived from the ITER blanket module CAD data, is used for evaluating the fast ion wall loads. The effect of the test blanket module is studied for both overall confinement and possible hot spots. The study indicates that the test blanket modules do not significantly deteriorate the fast ion confinement.

Effect of plasma response on the fast ion losses due to ELM control coils in ITER

Mitigating edge localized modes (ELMs) with resonant magnetic perturbations (RMPs) can increase energetic particle losses and resulting wall loads, which have previously been studied in the vacuum approximation. This paper presents recent results of fusion alpha and NBI ion losses in the ITER baseline scenario modelled with the Monte Carlo orbit following code ASCOT in a realistic magnetic field including the effect of the plasma response. The response was found to reduce alpha particle losses but increase NBI losses, with up to 4.2% of the injected power being lost. Additionally, some of the load in the divertor was found to be shifted away from the target plates toward the divertor dome.

An advection-diffusion model for cross-field runaway electron transport in perturbed magnetic fields

Disruption-generated runaway electrons (RE) present an outstanding issue for ITER. The predictive computational studies of RE generation rely on orbit-averaged computations and, as such, they lack the effects from the magnetic field stochasticity. Since stochasiticity is naturally present in post-disruption plasma, and externally induced stochastization offers a prominent mechanism to mitigate RE avalanche, we present an advection-diffusion model that can be used to couple an orbit-following code to an orbit-averaged tool in order to capture the cross-field transport and to overcome the latters limitation. The transport coefficients are evaluated via a Monte Carlo method. We show that the diffusion coefficient differs significantly from the well-known Rechester-Rosenbluth result. We also demonstrate the importance of including the advection: it has a two-fold role both in modelling transport barriers created by magnetic islands and in amplifying losses in regions where the islands are not present.

Modelling of 3D fields due to ferritic inserts and test blanket modules in toroidal geometry at ITER

Computations in toroidal geometry are systematically performed for the plasma response to 3D magnetic perturbations produced by ferritic inserts (FIs) and test blanket modules (TBMs) for four ITER plasma scenarios: the 15 MA baseline, the 12.5 MA hybrid, the 9 MA steady state, and the 7.5 MA half-field helium plasma. Due to the broad toroidal spectrum of the FI and TBM fields, the plasma response for all the n = 1-6 field components are computed and compared. The plasma response is found to be weak for the high-n (n > 4) components. The response is not globally sensitive to the toroidal plasma flow speed, as long as the latter is not reduced by an order of magnitude. This is essentially due to the strong screening effect occurring at a finite flow, as predicted for ITER plasmas. The ITER error field correction coils (EFCC) are used to compensate the n = 1 field errors produced by FIs and TBMs for the baseline scenario for the purpose of avoiding mode locking. It is found that the middle row of the EFCC, with a suitable toroidal phase for the coil current, can provide the best correction of these field errors, according to various optimisation criteria. On the other hand, even without correction, it is predicted that these n = 1 field errors will not cause substantial flow damping for the 15 MA baseline scenario.

Mechanics of ELM control coil induced fast particle transport in ITER

Using the orbit-following code ASCOT, we have modelled fast ion transport in ITER under the influence of ELM control coils (ECCs), toroidal field ripple, and test blanket modules, with emphasis on how the plasma response (PR) modifies the transport mechanisms and fast ion loads on the divertor. We found that while PR shields the plasma by healing broken flux surfaces at the plasma periphery, it also opens a new loss channel for marginally trapped particles: PR causes strong toroidal variation of the poloidal field near the X-point which leads to de-localisation of banana tips and collisionless transport. The reduction in passing particle losses and the increase in marginally trapped particle losses shift divertor loads from targets to the dome and under-the-dome structures. The plasma response was calculated by both MARS-F and JOREK codes. The new transport mechanism was stronger for PR calculated by JOREK which, unlike MARS-F, explicitly includes the X-point.

Protecting ITER walls: Fast ion power loads in 3D magnetic field

The fusion alpha and beam ion with steady-state power loads in all four main operating scenarios of ITER have been evaluated by the ASCOT code. For this purpose, high-fidelity magnetic backgrounds were reconstructed, taking into account even the internal structure of the ferritic inserts and tritium breeding modules (TBM). The beam ions were found to be almost perfectly confined in all scenarios, and only the so-called hybrid scenario featured alpha loads reaching 0.5 MW due to its more triangular plasma. The TBMs were not found to jeopardize the alpha confinement, nor cause any hot spots. Including plasma response did not bring dramatic changes to the load. The ELM control coils (ECC) were simulated in the baseline scenario and found to seriously deteriorate even the beam confinement. However, the edge perturbation in this case is so large that the sources have to be re-evaluated with plasma profiles that take into account the ECC perturbation.

Synthetic NPA diagnostic for energetic particles in JET plasmas

Neutral particle analysis (NPA) is one of the few methods for diagnosing fast ions inside a plasma by measuring neutral atom fluxes emitted due to charge exchange reactions. The JET tokamak feature ...

Effect of the European design of TBMs on ITER wall loads due to fast ions in the baseline (15 MA), hybrid (12.5 MA), steady-state (9 MA) and half-field (7.5 MA) scenarios

We assess the effect of the European design of the pebble-bed helium-cooled test blanket modules (TBM) on fast ion power loads on ITER material surfaces. For this purpose, the effect of not only the TBMs but also the ferritic inserts (FI), used for mitigating the toroidal field ripple, were included in unprecedented detail in the reconstruction of the 3-dimensional magnetic field. This is important because, due to their low collisionality, fast ions follow the magnetic geometry much more faithfully than the thermal plasma. The Monte Carlo orbit-following code ASCOT was used to simulate all the foreseen operating scenarios of ITER: the baseline 15 MA standard H-mode operation, the 12.5 MA hybrid scenario, the 9 MA advanced scenario, and the half-field scenario with helium plasma that will be ITERs initial operating scenario. The effect of TBMs was assessed by carrying out the simulations in pairs: one including only the effect of ferritic inserts, and the other including also the perturbation due to TBMs. Both thermonuclear fusion alphas and NBI ions from ITER heating beams were addressed. The TBMs are found to increase the power loads, but the absolute values remain small. Neither do they produce any additional hot spots.