Two (‘plus one’)-dimensional simulation of pellet cloud evolution in the poloidal plane with a prescribed neutral particle source strength

Abstract

Abstract. The evolution of pellet clouds in magnetically confined thermonuclear plasmas is studied by means of a time-dependent two-dimensional resistive MHD model applicable to the poloidal plane of a plasma torus. A massive neutral particle source representing a pellet traverses the plasma and continuously releases cold and unionized particles. Its motion is confined to a poloidal plane, which is thus considered to be a symmetry plane of the model. The conservation equations supplemented by Maxwell's equations, Ohm's generalized law, and a number of rate equations are solved for the symmetry plane. To each mesh point of the Eulerian grid in the poloidal plane, a toroidal 'flux tube' is attached. The field-aligned expansion of the ablated substance in these flux tubes and the corresponding change of the state parameters are computed in a Lagrangian approximation. Hence the two-dimensional Eulerian resistive MHD code is operated alternating with the one-dimensional Lagrangian routine. In the first series of computations, the neutral particle source strength is a prescribed input parameter, the applied magnetic field as well as the initial state parameters of the background plasma are uniform. Results of these calculations are presented and the solutions obtained are discussed.

Recent results on the fuelling and control of plasmas by pellet injection, application to ITER

“…Practically, the penetration depths calculated with these different models are within ∼20% and reproduce reasonably well the measurements in present day machines for a wide range of pellet and plasma parameters [6,8]. Finally, 2D-time dependent MHD models are presently being developed by several authors [9,10], which do not consider a priori a total decoupling between the spherically and longitudinally expanding parts of the cloud. Even if their present status does not yet allow a realistic simulation of a complete pellet ablation, it is shown in [9] that in the case of rapid heating of the cloud (e.g.…”

Pellet – Plasma Interaction: an Analysis of Pellet Injection Experiments by Means of a Multi‐Dimensional MHD Pellet Code

“…This dimension is a relevant quantity: it determines the local 'channel cross-section' for cloud expansion along the magnetic field lines. The numerical simulations performed with one-and also with two-dimensional MHD codes developed reproduce, approximately, the observed ionization radii and the associated strip widths (see [13][14][15][16], and [27,[29][30][31][32][33]). The slight curvature of the of the pellet trace towards the LFS may be due to asymmetric heating or the possible presence of drift.…”

“…Note that the necessity of using this preshield factor is caused by discretization along the pellet path in terms of the local ionization radii (flux tube radii). Applying a time-dependent self-consistent two-dimensional model to the poloidal plane [32], the ionization dynamics is calculated simultaneously for the whole plane thus making the introduction of the ionization radius as a discrete parameter superfluous. It should also be noted that modelling of pellet ablation in toroidal devices in a consistent way would require truly three-dimensional computations with full account of the presence of a high-density neutral gas component.…”

Μελέτη παραγωγής δέσμης αρνητικών ιόντων μεγάλου ρεύματος - μεγάλης ενέργειας και φωτο-ουδετεροποίησή της για τη χρήση σε αντιδραστήρες Tokamak

“…A multi-fluid, one dimensional code in cylindrical geometry is being developed (based on a multi-fluid plasma fusion code [21]) which describes the spatio-temporal evolution of positive, negative deuterium ions and electrons in a MID. The model equations [22] include conservation of particles, momentum and energy of electron and negative ions, coupled with Maxwell's equation for the space-charge separation. In the calculations presented here we consider that at time zero, equal densities of electrons (n e ) and positive (n p ), negative ions (n i ) are enclosed between the two electrodes (anode and cathode).…”

“…Στο χώρο μεταξύ των δύο κυλίνδρων γίνεται η επιτάχυνση των σωματιδίων. Ο εσωτερικός κύλινδρος είναι η κάθοδος (αρνητικό δυναμικό) και ο εξωτερικός η άνοδος (θετικό δυναμικό) ενώ το ομογενές εξωτερικό μαγνητικό πεδίο εφαρμόζεται παράλληλα στον άξονα z. μελέτη της χωροχρονικής εξέλιξης του πλάσματος που δημιουργείται εντός της διόδου θα γίνει με τη χρήση ενός μοντέλου και ενός αριθμητικού κώδικα multi-fluid (καθώς μπορεί να λαμβάνει υπόψη του διαφορετικά είδη σωματιδίων) σε μία διάσταση, προσαρμοσμένο για την μαγνητικά μονωμένη δίοδο από έναν κώδικα multifluid για πλάσμα σύντηξης[37][38][39]. Στις περισσότερες προσομοιώσεις εξετάζεται η περίπτωση που υπάρχουν ηλεκτρόνια και αρνητικά ιόντα σε κυλινδρική συμμετρία σε αντίστοιχο υπόβαθρο πλάσματος που εξασφαλίζει μακροσκοπικά την ουδετερότητα.Στο φυσικό πρόβλημα τα αρνητικά ιόντα παράγονται από το αρχικό πλάσμα, το οποίο στην προσομοίωση της λειτουργίας της διόδου ως μέσο επιτάχυνσης και εξαγωγής δεν χρειάζεται η περιγραφή του.Ο χρησιμοποιούμενος κώδικας βασίζεται σε ένα σύστημα εξισώσεων που προέρχονται από την αρχή της διατήρησης της μάζας, της ορμής, της ενέργειας σε συνδυασμό με τις εξισώσεις του Maxwell και του Poisson.…”