Plasma simulation as eigenvalue problem

Knorr, G.; Shoucri, M.

doi:10.2172/4474894

Cited by 8 publications

(19 citation statements)

References 4 publications

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“…Without careful velocity-scaling of the Hermite functions, however, fine-scales develop at the level of the coarse velocity grid, requiring spectral expansions ranging from 500 to 1500 Hermite modes to achieve only moderate accuracy levels [21,25,26]. To alleviate this requirement, some of these earlier FH algorithms incorporated artificial damping or monotonic reduction of the Hermite expansion order N u over time [14,[25][26][27]; unfortunately, artificial damping changes the interesting collisionless physics and decreasing N u eventually leaves the simulation with no velocity resolution whatsoever.…”

Section: Introductionmentioning

confidence: 99%

Vlasov Simulations Using Velocity-Scaled Hermite Representations

Schumer

Holloway²

1998

Journal of Computational Physics

110

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Section: Introductionmentioning

confidence: 99%

Vlasov Simulations Using Velocity-Scaled Hermite Representations

Schumer

Holloway²

1998

Journal of Computational Physics

110

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“…The numerical problems associated with the long-term behavior are typical in Vlasov solvers which utilize the truncated expansions of the distribution function. A commonly used solution is the introduction of the arti cial attenuation term of a Fokker-Planck t ype 46,71]. We use a similar approach to suppress the unphysical growth and introduce an arti cial attenuation term in our dynamical system.…”

Section: Numerical Integration Of the Coupled Moment Equations 321 mentioning

confidence: 99%

“…In contrast with the approach of Ref. 46,71], a diagonal relaxation term ;; kl a kl kl mn , i s i n troduced on the right-hand side of Eq. (3.21) with the phenomenological damping coe cient ; kl = e (k+l;2) 2 = 2 ; 1:…”

Section: Numerical Integration Of the Coupled Moment Equations 321 mentioning

confidence: 99%

Collisionless relaxation in beam-plasma systems

Backhaus

2001

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This thesis reports the results from the theoretical investigations, both numerical and analytical, of collisionless relaxation phenomena in beam-plasma systems. Many results of this work can also be applied to other lossless systems of plasma physics, beam physics and astrophysics.Di erent aspects of the physics of collisionless relaxation and its modeling are addressed. A new theoretical framework, named Coupled Moment Equations (CME), is derived and used in numerical and analytical studies of the relaxation of second order moments such as beam size and emittance oscillations. This technique extends the well-known envelope equation formalism, and it can be applied to general systems with nonlinear forces. It is based on a systematic moment expansion of the Vlasov equation. In contrast to the envelope equation, which is derived assuming constant rms beam emittance, the CME model allows the emittance to vary through coupling to higher order moments. The CME model is implemented in slab geometry in the absence of return currents. The CME simulation yields rms beam sizes, velocity spreads and emittances that are in good agreement with particle-in-cell (PIC) simulations for a wide range of system parameters.The mechanism of relaxation is also considered within the framework of the CME system. It is discovered that the rapid relaxation or beam size oscillations can be attributed to a resonant coupling between di erent modes of the system. A simple analytical estimate of the relaxation time is developed.The nal state of the system reached after the relaxation is complete is investigated. New and accurate analytical results for the second order moments in the phase-mixed 2 state are obtained. Unlike previous results, these connect the nal values of the second order moments with the initial beam mismatch. These analytical estimates are in good agreement with the CME model and PIC simulations. Predictions for the nal density and temperature are developed that show main important features of the spatial dependence of the pro les. Di erent aspect of the nal coarse-grained state such as its non-thermal nature, the appearance of 'hot' regions on the periphery and the core-halo character of the density are investigated.Professor Jonathan S. Wurtele Dissertation Committee Chair iii To my grandmothers, whose di erent lives were always an inspiration...

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“…(3) in the form The study of such term for Hermite polynomials expansion has been given by Knorr and Shoucri [6-]. ·In order to get the same effects using the Chebyshev polynomials, we follow the same steps as in [6] and look for a "collision" operator C such·'that …”

Section: V=omentioning

confidence: 99%