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EUTERPE: Difference between revisions
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<ref>[http://pop.aip.org/phpaen/v8/i7/p3321_s1 G. Jost, T. M. Tran, W. Cooper, and K. Appert. Phys. Plasmas '''8''': 3321 (2001)]</ref> | <ref>[http://pop.aip.org/phpaen/v8/i7/p3321_s1 G. Jost, T. M. Tran, W. Cooper, and K. Appert. Phys. Plasmas '''8''': 3321 (2001)]</ref> | ||
<ref>[http://pop.aip.org/phpaen/v11/i6/p3196_s1 V. Kornilov, R. Kleiber, R. Hatzky, L. Villard, and G. Jost. Phys. Plasmas '''11''': 3196 (2004)]</ref> | <ref>[http://pop.aip.org/phpaen/v11/i6/p3196_s1 V. Kornilov, R. Kleiber, R. Hatzky, L. Villard, and G. Jost. Phys. Plasmas '''11''': 3196 (2004)]</ref> | ||
<ref>[http://iopscience.iop.org/0029-5515/45/4/003 V. Kornilov, R. Kleiber, and R. Hatzky, Nucl. Fusion '''45''': 238 (2005)]</ref><ref>[http:// | <ref>[http://iopscience.iop.org/0029-5515/45/4/003 V. Kornilov, R. Kleiber, and R. Hatzky, Nucl. Fusion '''45''': 238 (2005)]</ref> | ||
axisymmetric equilibria | <ref>[http://link.aip.org/link/?APCPCS/871/136/1 R. Kleiber, ''Global linear gyrokinetic simulations for stellarator and axisymmetric equilibria'', Joint Varenna-Lausanne International Workshop. AIP Conference Proceedings, 871, p. 136, 2006]</ref>. | ||
AIP Conference Proceedings, 871, p. 136, 2006]</ref>. Afterwards, the code has been heavily optimized and improved. The perturbation to the magnetic field, a third species (in adition to electrons and ions) and the non-linear dynamics have been included. | Afterwards, the code has been heavily optimized and improved. The perturbation to the magnetic field, a third species (in adition to electrons and ions) and the non-linear dynamics have been included. | ||
The EUTERPE code solves the gyroaveraged Vlasov equation for the distribution function of ions | The EUTERPE code solves the gyroaveraged Vlasov equation for the distribution function of ions | ||
<math> | :<math> | ||
\frac{\partial f}{\partial t} + \frac{\rm{d}v_{||}}{\rm{d}t} \frac{\partial f}{\partial v_{||}} + \frac{\rm{d}\vec{R}}{\rm{d}t} \frac{\partial f}{\partial \vec{R}} = 0 | \frac{\partial f}{\partial t} + \frac{\rm{d}v_{||}}{\rm{d}t} \frac{\partial f}{\partial v_{||}} + \frac{\rm{d}\vec{R}}{\rm{d}t} \frac{\partial f}{\partial \vec{R}} = 0 | ||
</math> | </math> | ||
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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> | :<math> | ||
f(\vec R, v_{||}, \mu, t) = f_{0}(\vec R, v_{||}, v_{\perp})+ \delta f(\vec R, v_{||}, \mu, t) | f(\vec R, v_{||}, \mu, t) = f_{0}(\vec R, v_{||}, v_{\perp})+ \delta f(\vec R, v_{||}, \mu, t) | ||
</math> | </math> | ||
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Each marker along with its weight is evolved following the particle trayectories and contributes a part to the distribution function, so that | 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> | ||