TURBULENT DIFFUSION OF TEST PARTICLES IN STRONGLY MAGNETIZED PLASMAS

1991 ◽  
Vol 05 (08) ◽  
pp. 1243-1262 ◽  
Author(s):  
MAURIZIO OTTAVIANI ◽  
MARCO PETTINI
Keyword(s):  
Electric Field ◽  
Equations Of Motion ◽  
Charged Particles ◽  
Mean Square Displacement ◽  
Wave Model ◽  
Particle Dynamics ◽  
Suitable Parameter ◽  
Test Particles ◽  
The Mean ◽  
Parameter Values

The motion of charged particles is described in the presence of a strong magnetic field and of an electric field made of three spatial Fourier modes whose amplitudes vary in time. The dynamics of the wave amplitudes is governed by a model of three interacting drift waves. For suitable parameter values of the three-wave model, chaotic solutions are found so that the Eulerian electric field is made of three turbulent modes. The E × B motion is described for charged particles in the guiding center approximation, which brings to nonlinear Hamiltonian equations of motion. The Hamiltonian (that coincides with the electric potential) is explicitly time-dependent through the temporal variation of the mode-amplitudes of the electric field, this fact is at the origin of the intrinsic chaoticity of particle dynamics (lagrangian chaos). Diffusive behaviour of particle trajectories is due to their intrinsic chaoticity and thus it is of non-collisional origin. Some results are reported concerning the particle dynamics when the Eulerian electric field is either quasi-periodically or chaotically varying in time. In particular, one finds different diffusion laws in the two cases (anomalous and classical respectively). The scaling behaviour of the diffusion coefficients (when the mean square displacement grows linearly in time) is reported. A simple stochastic model is also used to account for some of the observed features of particle diffusion.

Ion acceleration by multiple laser pulses and their spontaneous electromagnetic fields in plasma

2008 ◽  
Vol 74 (1) ◽  
pp. 111-118
Author(s):  
FEN-CE CHEN
Keyword(s):  
Magnetic Fields ◽  
Electric Field ◽  
Analytical Model ◽  
Electromagnetic Fields ◽  
Equations Of Motion ◽  
Charged Particles ◽  
Laser Pulses ◽  
The Self ◽  
Electric And Magnetic Fields ◽  
Relativistic Equations

AbstractThe acceleration of ions by multiple laser pulses and their spontaneously generated electric and magnetic fields is investigated by using an analytical model for the latter. The relativistic equations of motion of test charged particles are solved numerically. It is found that the self-generated axial electric field plays an important role in the acceleration, and the energy of heavy test ions can reach several gigaelectronvolts.

Numerische Untersuchungen charakteristischer Größen eines Plasmamodells

1968 ◽  
Vol 23 (5) ◽  
pp. 761-770
Author(s):  
Karlheinz Wilke
Keyword(s):  
Electric Field ◽  
Relaxation Times ◽  
Charged Particles ◽  
Density Fluctuations ◽  
Distribution Functions ◽  
Mean Square ◽  
3 Dimensional ◽  
Time Averages ◽  
The Mean ◽  
Predictor Corrector

A fully 3-dimensional plasma consisting of up to 96 charged particles is simulated in a computer. The plasma is confined to a sphere (or cube) with specularly reflecting walls. The forces are computed using a predictor corrector method with variable time steps. From initial configurations randomly chosen the evolution of the plasma is followed numerically. Distribution functions and moments with respect to various phase variables are obtained as time averages: the distribution of velocity, kinetic and potential energy, of the electric microfield, the micropotential as measured at a neutral point of reference (usually the center of the system) , the mean square electric field, the microfield correlation function and the particle relaxation times. As the sphere used in the experiments has dimensions only slightly larger than the Debye sphere, collective phenomena and those due to major density fluctuations cannot be expected. Despite these limitations the mean electric field is found to be high by approx. 10% compared to the Holtsmark field. Furthermore other comparisons to existing theories with respect to the variables already mentioned are carried out.

QUANTUM COHERENCE OF SUPERLATTICES IN TRIANGLE-WAVE ELECTRIC FIELDS

2000 ◽  
Vol 14 (01) ◽  
pp. 41-49 ◽  
Author(s):  
HAI-FENG LIU ◽  
XIAN-GENG ZHAO
Keyword(s):  
Electric Field ◽  
Exact Solutions ◽  
Electric Fields ◽  
Quantum Coherence ◽  
Mean Square Displacement ◽  
Initial Distribution ◽  
Coherent Motion ◽  
Mean Square ◽  
Long Period ◽  
The Mean

The problem of coherent motion of an electron in a long period superlattice driven by a triangle-wave electric field is studied. Exact solutions for the amplitude propagators, the field-induced polarization, the mean-square displacement, and the quasienergy spectrum of any initial distribution and long-range hopping coupling are obtained generally. Total collapse of the quasienergy spectrum is found to take place at certain field parameters, which leads to the transition between localization and delocalization. The transport property of the system is also investigated.

DIFFUSING WAVE SPECTROSCOPY STUDY OF TAILING PHENOMENON OF COLLOIDAL ELECTRORHEOLOGY FLUIDS

2005 ◽  
Vol 19 (07n09) ◽  
pp. 1243-1248
Author(s):  
Y. H. MA ◽  
L. M. GUO ◽  
L. ZHONG ◽  
L. W. ZHOU
Keyword(s):  
Electric Field ◽  
Colloidal Particles ◽  
Mean Square Displacement ◽  
Electrorheological Fluid ◽  
Mean Square ◽  
Diffusing Wave Spectroscopy ◽  
Fluid Systems ◽  
The Mean ◽  
Electric Filed ◽  
Er Fluid

Back scattering of diffusing wave spectroscopy (DWS) method is employed to measure the mean square displacements of the colloidal particles in electrorheological fluid systems right after an electric field is applied and removed. An electrorheological fluid consisting of colloidal particles 30-40 nm in size shows a tailing phenomenon, namely the clusters of the colloidal ER particles do not return to their original state of Brownian motion as soon as the electric filed is removed. The DWS results of above ER fluid shows that the mean square displacement remains small and changes slowly with time right after the electric field is removed. The Van der Waals attractive force between colloidal particles is used to explain this tailing phenomenon.

Dynamics of collisional particles in a fluctuating magnetic field

1995 ◽  
Vol 54 (3) ◽  
pp. 333-371 ◽  
Author(s):  
F. Spineanu ◽  
M. Vlad
Keyword(s):  
Magnetic Field ◽  
Equations Of Motion ◽  
Analytical Calculation ◽  
Mean Square Displacement ◽  
Random Processes ◽  
Functional Formalism ◽  
Velocity Fluctuations ◽  
The Mean ◽  
Stochastic Magnetic Field ◽  
Spectral Cut

The equations of motion of a test particle in a stochastic magnetic field and interacting through collisions with a plasma are Langevin-type equations. Under reasonable assumptions on the statistical properties of the random processes (field and collisional velocity fluctuations), we perform an analytical calculation of the mean-square displacement (MSD) of the particle. The basic nonlinearity in the problem (Lagrangian argument of the random field) yields complicated averages, which we carry out using a functional formalism. The result is expressed as a series, and we find the conditions for its convergence, i.e. the limits of validity of our approach (essentially, we must restrict attention to non-chaotic regimes). Further, employing realistic bounds (spectral cut-off and limited time of observation), we derive an explicit formula for the MSD. We show that from this unique expression, we can obtain several previously known results.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

Effect of external magnetic field on lane formation in driven pair-ion plasmas

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
Swati Baruah ◽  
U. Sarma ◽  
R. Ganesh
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Field Strength ◽  
Electric Field ◽  
Electric Field Strength ◽  
Coupling Parameter ◽  
Critical Parameters ◽  
Coulomb Coupling ◽  
Lane Formation ◽  
Parameter Values

Lane formation dynamics in externally driven pair-ion plasma (PIP) particles is studied in the presence of external magnetic field using Langevin dynamics (LD) simulation. The phase diagram obtained distinguishing the no-lane and lane states is systematically determined from a study of various Coulomb coupling parameter values. A peculiar lane formation-disintegration parameter space is identified; lane formation area extended to a wide range of Coulomb coupling parameter values is observed before disappearing to a mixed phase. The different phases are identified by calculating the order parameter. This and the critical parameters are calculated directly from LD simulation. The critical electric field strength value above which the lanes are formed distinctly is obtained, and it is observed that in the presence of the external magnetic field, the PIP system requires a higher value of the electric field strength to enter into the lane formation state than that in the absence of the magnetic field. We further find out the critical value of electric field frequency beyond which the system exhibits a transition back to the disordered state and this critical frequency is found as an increasing function of the electric field strength in the presence of an external magnetic field. The movement of the lanes is also observed in a direction perpendicular to that of the applied electric and magnetic field directions, which reveals the existence of the electric field drift in the system under study. We also use an oblique force field as the external driving force, both in the presence and absence of the external magnetic field. The application of this oblique force changes the orientation of the lane structures for different applied oblique angle values.

scholarly journals Quantifying the Effects of Wave—Current Interactions on Tidal Energy Resource at Sites in the English Channel Using Coupled Numerical Simulations

Energies ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3625
Author(s):  
Jon Hardwick ◽  
Ed B. L. Mackay ◽  
Ian G. C. Ashton ◽  
Helen C. M. Smith ◽  
Philipp R. Thies
Keyword(s):  
Wave Model ◽  
Tidal Energy ◽  
English Channel ◽  
Flow Conditions ◽  
Mean Flow ◽  
Radiation Stress ◽  
Large Wave ◽  
Stress Gradients ◽  
The Mean ◽  
Flow Power

Numerical modeling of currents and waves is used throughout the marine energy industry for resource assessment. This study compared the output of numerical flow simulations run both as a standalone model and as a two-way coupled wave–current simulation. A regional coupled flow-wave model was established covering the English Channel using the Delft D-Flow 2D model coupled with a SWAN spectral wave model. Outputs were analyzed at three tidal energy sites: Alderney Race, Big Roussel (Guernsey), and PTEC (Isle of Wight). The difference in the power in the tidal flow between coupled and standalone model runs was strongly correlated to the relative direction of the waves and currents. The net difference between the coupled and standalone runs was less than 2.5%. However, when wave and current directions were aligned, the mean flow power was increased by up to 7%, whereas, when the directions were opposed, the mean flow power was reduced by as much as 9.6%. The D-Flow Flexible Mesh model incorporates the effects of waves into the flow calculations in three areas: Stokes drift, forcing by radiation stress gradients, and enhancement of the bed shear stress. Each of these mechanisms is discussed. Forcing from radiation stress gradients is shown to be the dominant mechanism affecting the flow conditions at the sites considered, primarily caused by dissipation of wave energy due to white-capping. Wave action is an important consideration at tidal energy sites. Although the net impact on the flow power was found to be small for the present sites, the effect is site specific and may be significant at sites with large wave exposure or strong asymmetry in the flow conditions and should thus be considered for detailed resource and engineering assessments.

scholarly journals Reconstruction of Diffusion Coefficients and Power Exponents from Single Lagrangian Trajectories

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 111
Author(s):  
Leonid M. Ivanov ◽  
Collins A. Collins ◽  
Tetyana Margolina
Keyword(s):  
Black Sea ◽  
Diffusion Coefficients ◽  
Current System ◽  
Mean Square Displacement ◽  
California Current ◽  
The Black Sea ◽  
Mean Square ◽  
California Current System ◽  
The Mean ◽  
Non Gaussian

Using discrete wavelets, a novel technique is developed to estimate turbulent diffusion coefficients and power exponents from single Lagrangian particle trajectories. The technique differs from the classical approach (Davis (1991)’s technique) because averaging over a statistical ensemble of the mean square displacement (<X2>) is replaced by averaging along a single Lagrangian trajectory X(t) = {X(t), Y(t)}. Metzler et al. (2014) have demonstrated that for an ergodic (for example, normal diffusion) flow, the mean square displacement is <X2> = limT→∞τX2(T,s), where τX2 (T, s) = 1/(T − s) ∫0T−s(X(t+Δt) − X(t))2 dt, T and s are observational and lag times but for weak non-ergodic (such as super-diffusion and sub-diffusion) flows <X2> = limT→∞≪τX2(T,s)≫, where ≪…≫ is some additional averaging. Numerical calculations for surface drifters in the Black Sea and isobaric RAFOS floats deployed at mid depths in the California Current system demonstrated that the reconstructed diffusion coefficients were smaller than those calculated by Davis (1991)’s technique. This difference is caused by the choice of the Lagrangian mean. The technique proposed here is applied to the analysis of Lagrangian motions in the Black Sea (horizontal diffusion coefficients varied from 105 to 106 cm2/s) and for the sub-diffusion of two RAFOS floats in the California Current system where power exponents varied from 0.65 to 0.72. RAFOS float motions were found to be strongly non-ergodic and non-Gaussian.

scholarly journals Towards bio-inspired artificial muscle: a mechanism based on electro-osmotic flow simulated using dissipative particle dynamics

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ramin Zakeri
Keyword(s):  
Zeta Potential ◽  
Electric Field ◽  
Dissipative Particle Dynamics ◽  
Artificial Muscle ◽  
Particle Dynamics ◽  
Polymer Membrane ◽  
Channel Width ◽  
Micro Channel ◽  
Osmotic Flow ◽  
Electro Osmotic Flow

AbstractOne of the unresolved issues in physiology is how exactly myosin moves in a filament as the smallest responsible organ for contracting of a natural muscle. In this research, inspired by nature, a model is presented consisting of DPD (dissipative particle dynamics) particles driven by electro-osmotic flow (EOF) in micro channel that a thin movable impermeable polymer membrane has been attached across channel width, thus momentum of fluid can directly transfer to myosin stem. At the first, by validation of electro-osmotic flow in micro channel in different conditions with accuracy of less than 10 percentage error compared to analytical results, the DPD results have been developed to displacement of an impermeable polymer membrane in EOF. It has been shown that by the presence of electric field of 250 V/m and Zeta potential − 25 mV and the dimensionless ratio of the channel width to the thickness of the electric double layer or kH = 8, about 15% displacement in 8 s time will be obtained compared to channel width. The influential parameters on the displacement of the polymer membrane from DPD particles in EOF such as changes in electric field, ion concentration, zeta potential effect, polymer material and the amount of membrane elasticity have been investigated which in each cases, the radius of gyration and auto correlation velocity of different polymer membrane cases have been compared together. This simulation method in addition of probably helping understand natural myosin displacement mechanism, can be extended to design the contraction of an artificial muscle tissue close to nature.

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