C. Zucca | Searcharxiv

arXiv2019

Exact simulation of first exit times for one-dimensional diffusion processes

The simulation of exit times for diffusion processes is a challenging task since it concerns many applications in different fields like mathematical finance, neuroscience, reliability... The usual procedure is to use discretiza-tion schemes which unfortunately introduce some error in the target distribution. Our aim is to present a new algorithm which simulates exactly the exit time for one-dimensional diffusions. This acceptance-rejection algorithm requires to simulate exactly the exit time of the Brownian motion on one side and the Brownian position at a given time, constrained not to have exit before, on the other side. Crucial tools in this study are the Girsanov transformation, the convergent series method for the simulation of random variables and the classical rejection sampling. The efficiency of the method is described through theoretical results and numerical examples.

math.PR↗

arXiv2013

Power requirements for electron cyclotron current drive and ion cyclotron resonance heating for sawtooth control in ITER

13MW of electron cyclotron current drive (ECCD) power deposited inside the q = 1 surface is likely to reduce the sawtooth period in ITER baseline scenario below the level empirically predicted to trigger neo-classical tearing modes (NTMs). However, since the ECCD control scheme is solely predicated upon changing the local magnetic shear, it is prudent to plan to use a complementary scheme which directly decreases the potential energy of the kink mode in order to reduce the sawtooth period. In the event that the natural sawtooth period is longer than expected, due to enhanced alpha particle stabilisation for instance, this ancillary sawtooth control can be provided from > 10MW of ion cyclotron resonance heating (ICRH) power with a resonance just inside the q = 1 surface. Both ECCD and ICRH control schemes would benefit greatly from active feedback of the deposition with respect to the rational surface. If the q = 1 surface can be maintained closer to the magnetic axis, the efficacy of ECCD and ICRH schemes significantly increases, the negative effect on the fusion gain is reduced, and off-axis negative-ion neutral beam injection (NNBI) can also be considered for sawtooth control. Consequently, schemes to reduce the q = 1 radius are highly desirable, such as early heating to delay the current penetration and, of course, active sawtooth destabilisation to mediate small frequent sawteeth and retain a small q = 1 radius.

physics.plasm-ph↗