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The code is based on the particle-in-cell (PIC) scheme, where the distribution function is discretized using markers. The δf approximation is used, so that the distribution function is decomposed in an equilibrium part (Maxwellian) and a time-dependent perturbation. | The code is based on the particle-in-cell (PIC) scheme, where the distribution function is discretized using markers. The δf approximation is used, so that the distribution function is decomposed in an equilibrium part (Maxwellian) and a time-dependent perturbation. | ||
<math> | |||
f(\vec R, v_{||}, \mu, t) = f_{0}(\vec R, v_{||}, v_{\perp})+ \delta f(\vec R, v_{||}, \mu, t) | |||
</math> | |||
Each marker along with its weight is evolved following the particle trayectories and contributes a part to the distribution function, so that | |||
<math> | <math> | ||
\delta f = \sum_{p=1} ^{N} w_p \delta ^{3}(\vec R - \vec R_p)\delta(v_{||} - v_{||p})\delta(\mu - \mu_p) /(2 \pi B), | \delta f = \sum_{p=1} ^{N} w_p \delta ^{3}(\vec R - \vec R_p)\delta(v_{||} - v_{||p})\delta(\mu - \mu_p) /(2 \pi B), | ||
</math> | </math> | ||
where the $w_p$ are the weights (contribution to the distribution function) associated to each marker. | |||
The electric potential is represented on a spatial grid, the electric charge being carried by the markers. Two coordinate systems are used in the code: a system of magnetic coordinates (PEST) $(s, \theta,\phi )$ is used for the electrostatic potential and cylindrical coordinates $(r, z,\phi )$ are used for pushing the particles, where $s=\Psi / \Psi_0$ is the normalized toroidal flux. The change between coordinate systems, which is facilitated by the existence of the common coordinate ($\phi$), is done in a continuous way. The equation for the field is discretized using finite elements (B-splines) and the PETSc library is used for solving it. The integration of the motion is done using a fourth order Runge-Kutta scheme. | |||
In linear simulations a phase factor transformation can be used and the equations can be integrated using a predictor-corrector scheme. These options have not been used in this work. | |||
An equilibrium state calculated with the code VMEC is used as a starting point. The equilibrium quantities computed by VMEC are mapped onto the spatial grid using an intermediate program. EUTERPE features several techniques for the noise control: the filtering of Fourier modes (square and diagonal filters can be used) and the optimized loading <ref>[http://pop.aip.org/phpaen/v9/i3/p898_s1 Hatzky, R Tran, TM Konies, A Kleiber, R Allfrey, SJ .Energy conservation in a nonlinear gyrokinetic particle-in-cell code for ion-temperature-gradient-driven modes in theta-pinch geometry. PHYSICS OF PLASMAS, 9- 3,p. 912,2002.]</ref>. More details about the code can be found in the Refs~\cite{EUTERPE:Jost,EUTERPE:Jost2,EUTERPE:Kornilov04,EUTERPE:Kornilov05,EUTERPE:Kleiber06} | |||
==References== | ==References== | ||
<references /> | <references /> | ||