Realistic Mass Ratio Research Articles

Introduction of temporal sub-stepping in the Multi-Level Multi-Domain semi-implicit Particle-In-Cell code Parsek2D-MLMD

In this paper, the introduction of temporal sub-stepping in Multi-Level Multi-Domain (MLMD) simulations of plasmas is discussed. The MLMD method addresses the multi-scale nature of space plasmas by simulating a problem at different levels of resolution. A large-domain “coarse grid” is simulated with low resolution to capture large-scale, slow processes. Smaller scale, local processes are obtained through a “refined grid” which uses higher resolution. Very high jumps in the resolution used at the different levels can be achieved thanks to the Implicit Moment Method and appropriate grid interlocking operations. Up to now, the same time step was used at all the levels. Now, with temporal sub-stepping, the different levels can also benefit from the use of different temporal resolutions. This saves further resources with respect to “traditional” simulations done using the same spatial and temporal stepping on the entire domain. It also prevents the levels from working at the limits of the stability condition of the Implicit Moment Method. The temporal sub-stepping is tested with simulations of magnetic reconnection in space. It is shown that, thanks to the reduced costs of MLMD simulations with respect to single-level simulations, it becomes possible to verify with realistic mass ratios scaling laws previously verified only for reduced mass ratios. Performance considerations are also provided.

Synergistic cross-scale coupling of turbulence in a tokamak plasma

For the first time, nonlinear gyrokinetic simulations spanning both the ion and electron spatio-temporal scales have been performed with realistic electron mass ratio ((mD∕me)1∕2 = 60.0), realistic geometry, and all experimental inputs, demonstrating the coexistence and synergy of ion (kθρs∼O(1.0)) and electron-scale (kθρe∼O(1.0)) turbulence in the core of a tokamak plasma. All multi-scale simulations utilized the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] to study the coupling of ion and electron-scale turbulence in the core (r/a = 0.6) of an Alcator C-Mod L-mode discharge shown previously to exhibit an under-prediction of the electron heat flux when using simulations only including ion-scale turbulence. Electron-scale turbulence is found to play a dominant role in setting the electron heat flux level and radially elongated (kr ≪ kθ) “streamers” are found to coexist with ion-scale eddies in experimental plasma conditions. Inclusion of electron-scale turbulence in these simulations is found to increase both ion and electron heat flux levels by enhancing the transport at the ion-scale while also driving electron heat flux at sub-ρi scales. The combined increases in the low and high-k driven electron heat flux may explain previously observed discrepancies between simulated and experimental electron heat fluxes and indicates a complex interaction of short and long wavelength turbulence.

Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem

We study the dynamics of the restricted planar three-body problem near mean motion resonances, i.e. a resonance involving the Keplerian periods of the two lighter bodies revolving around the most massive one. This problem is often used to model Sun–Jupiter–asteroid systems. For the primaries (Sun and Jupiter), we pick a realistic mass ratio \mu=10^{-3} and a small eccentricity e_0>0 . The main result is a construction of a variety of non local diffusing orbits which show a drastic change of the osculating (instant) eccentricity of the asteroid, while the osculating semi major axis is kept almost constant. The proof relies on the careful analysis of the circular problem, which has a hyperbolic structure, but for which diffusion is prevented by KAM tori. In the proof we verify certain non-degeneracy conditions numerically. Based on the work of Treschev, it is natural to conjecture that the time of diffusion for this problem is \sim \frac{-\ln (\mu e_0)}{\mu^{3/2} e_0} . We expect our instability mechanism to apply to realistic values of e_0 and we give heuristic arguments in its favor. If so, the applicability of Nekhoroshev theory to the three-body problem as well as the long time stability become questionable. It is well known that, in the Asteroid Belt, located between the orbits of Mars and Jupiter, the distribution of asteroids has the so-called Kirkwood gaps exactly at mean motion resonances of low order. Our mechanism gives a possible explanation of their existence. To relate the existence of Kirkwood gaps with Arnol'd diffusion, we also state a conjecture on its existence for a typical \epsilon -perturbation of the product of the pendulum and the rotator. Namely, we predict that a positive conditional measure of initial conditions concentrated in the main resonance exhibits Arnol’d diffusion on time scales \frac{- \ln \epsilon }{\epsilon^{2}} .

RECONNECTION AND ELECTRON TEMPERATURE ANISOTROPY IN SUB-PROTON SCALE PLASMA TURBULENCE

Turbulent behavior at sub-proton scales in magnetized plasmas is important for a full understanding of the energetics of astrophysical flows such as the solar wind. We study the formation of electron temperature anisotropy due to reconnection in the turbulent decay of sub-proton scale fluctuations using two dimensional, particle-in-cell (PIC) plasma simulations with realistic electron-proton mass ratio and a guide field out of the simulation plane. A fluctuation power spectrum with approximately power law form is created down to scales of order the electron gyroradius. In the dynamic magnetic field topology, which gradually relaxes in complexity, we identify the signatures of collisionless reconnection at sites of X-point field geometry. The reconnection sites are generally associated with regions of strong parallel electron temperature anisotropy. The evolving topology of magnetic field lines connected to a reconnection site allows spatial mixing of electrons accelerated at multiple, spatially separated reconnection regions. This leads to the formation of multi-peaked velocity distribution functions with a strong parallel temperature anisotropy. In a three-dimensional system, supporting the appropriate wave vectors, the multi-peaked distribution functions would be expected to be unstable to kinetic instabilities, contributing to dissipation. The proposed mechanism of anisotropy formation is also relevant to space and astrophysical systems where the evolution of the plasma is constrained by linear temperature anisotropy instability thresholds. The presence of reconnection sites leads to electron energy gain, nonlocal velocity space mixing and the formation of strong temperature anisotropy; this is evidence of an important role for reconnection in the dissipation of turbulent fluctuations.

An asymptotic safety scenario for gauged chiral Higgs–Yukawa models

We investigate chiral Higgs-Yukawa models with a non-abelian gauged left-handed sector reminiscent to a sub-sector of the standard model. We discover a new weak-coupling fixed-point behavior that allows for ultraviolet complete RG trajectories which can be connected with a conventional long-range infrared behavior in the Higgs phase. This non-trivial ultraviolet behavior is characterized by asymptotic freedom in all interaction couplings, but a quasi conformal behavior in all mass-like parameters. The stable microscopic scalar potential asymptotically approaches flatness in the ultraviolet, however, with a non-vanishing minimum increasing inversely proportional to the asymptotically free gauge coupling. This gives rise to nonperturbative -- though weak-coupling -- threshold effects which induce ultraviolet stability along a line of fixed points. Despite the weak-coupling properties, the system exhibits non-Gaussian features which are distinctly different from its standard perturbative counterpart: e.g., on a branch of the line of fixed points, we find linear instead of quadratically running renormalization constants. Whereas the Fermi constant and the top mass are naturally of the same order of magnitude, our model generically allows for light Higgs boson masses. Realistic mass ratios are related to particular RG trajectories with a "walking" mid-momentum regime.

Black-hole–neutron-star mergers at realistic mass ratios: Equation of state and spin orientation effects

Black-hole--neutron-star mergers resulting in the disruption of the neutron star and the formation of an accretion disk and/or the ejection of unbound material are prime candidates for the joint detection of gravitational-wave and electromagnetic signals when the next generation of gravitational-wave detectors comes online. However, the disruption of the neutron star and the properties of the postmerger remnant are very sensitive to the parameters of the binary (mass ratio, black-hole spin, neutron star radius). In this paper, we study the impact of the radius of the neutron star and the alignment of the black-hole spin on black-hole--neutron-star mergers within the range of mass ratio currently deemed most likely for field binaries (${M}_{\mathrm{BH}}\ensuremath{\sim}7{M}_{\mathrm{NS}}$) and for black-hole spins large enough for the neutron star to disrupt (${J}_{\mathrm{BH}}/{M}_{\mathrm{BH}}^{2}=0.9$). We find that (i) In this regime, the merger is particularly sensitive to the radius of the neutron star, with remnant masses varying from $0.3{M}_{\mathrm{NS}}$ to $0.1{M}_{\mathrm{NS}}$ for changes of only 2 km in the NS radius; (ii) $0.01{M}_{\ensuremath{\bigodot}}--0.05{M}_{\ensuremath{\bigodot}}$ of unbound material can be ejected with kinetic energy $\ensuremath{\gtrsim}{10}^{51}\text{ }\text{ }\mathrm{ergs}$, a significant increase compared to low mass ratio, low spin binaries. This ejecta could power detectable postmerger optical and radio afterglows. (iii) Only a small fraction of the Advanced LIGO events in this parameter range have gravitational-wave signals which could offer constraints on the equation of state of the neutron star (at best $\ensuremath{\sim}3%$ of the events for a single detector at design sensitivity). (iv) A misaligned black-hole spin works against disk formation, with less neutron-star material remaining outside of the black hole after merger, and a larger fraction of that material remaining in the tidal tail instead of the forming accretion disk. (v) Large kicks ${v}_{\mathrm{kick}}\ensuremath{\gtrsim}300\text{ }\text{ }\mathrm{km}/\mathrm{s}$ can be given to the final black hole as a result of a precessing black-hole--neutron-star merger, when the disruption of the neutron star occurs just outside or within the innermost stable spherical orbit.

PARTICLE-IN-CELL SIMULATIONS OF PARTICLE ENERGIZATION VIA SHOCK DRIFT ACCELERATION FROM LOW MACH NUMBER QUASI-PERPENDICULAR SHOCKS IN SOLAR FLARES

Low Mach number, high beta fast mode shocks can occur in the magnetic reconnection outflows of solar flares. These shocks, which occur above flare loop tops, may provide the electron energization responsible for some of the observed hard X-rays and contemporaneous radio emission. Here we present new 2D particle-in-cell simulations of low Mach number/high beta quasi-perpendicular shocks. The simulations show that electrons above a certain energy threshold experience shock-drift-acceleration. The transition energy between the thermal and non-thermal spectrum and the spectral index from the simulations are consistent with some of the X-ray spectra from RHESSI in the energy regime of $E\lesssim 40\sim 100$ keV. Plasma instabilities associated with the shock structure such as the modified-two-stream and the electron whistler instabilities are identified using numerical solutions of the kinetic dispersion relations. We also show that the results from PIC simulations with reduced ion/electron mass ratio can be scaled to those with the realistic mass ratio.

The impact of turbulence on electron heating and acceleration near the neutral point of externally driven reconnecting current sheets in solar flares

We aim to investigate the influence of plasma instability on electron acceleration and heating near the neutral point of a turbulent reconnecting current sheet (RCS). Through numerically solving the one dimensional relativistic Vlasov equation with typical solar coronal parameters and a realistic mass ratio in the presence of a strong inductive electric field E0, we suggest that the wave-particle scattering may produce a flat electron flux spectrum from thermal to nonthermal electrons without a sudden low-energy cutoff in the acceleration region. The ratio between electron heating and acceleration decreases with the increase of the induced electric field. It is about one for E0=1 V cm−1 and one fourth for E0=10 V cm−1. The unstable waves excited by the beam plasma instability first accelerate the electrons, then trap these electrons from further acceleration by an induced electric field through wave-particle resonant interactions.

Nonlinear dependence of anomalous resistivity on the reconnecting electric field in the Earth’s magnetotail

Based upon the observational data of the fast magnetic reconnection in the nearly collisionless magnetotail and the particle in cell (PIC) simulations on the electron acceleration in the reconnecting current sheet with guide magnetic field, we self consistently solved one dimension Vlasov equation with the magnetotail parameters and realistic mass ratio to explore the relationship between the anomalous resistivity and the induced electric field. As compared with theoretic formula for the current driven ion-acoustic and Buneman anomalous resistivity, the anomalous resistivity may result from the ion acoustic instability for small reconnecting electric field and the Buneman instability for large reconnecting electric field. The discrepancy between the theoretic results and numerical simulations may be caused by the high frequency instability that results from the deviation of electron distribution from Maxwellian one. These results are consistent with the early experimental results and favorable for the fast reconnection to take place.

Enhancement in the electromagnetic beam-plasma instability due to ion streaming

AbstractWe investigate the Weibel instability in counter-propagating electron–ion plasmas with focus on the ion contribution, considering a realistic mass ratio. A generalized dispersion relation is derived from the relativistic theory by assuming an initially anisotropic temperature, which is represented by a waterbag distribution in momentum space, which shows an enhanced growth rate due to ion response. Two-dimensional particle-in-cell simulations support the theoretical analysis, showing a further amplification of magnetic field on ion time scale. The effect of an initial anisotropic temperature is investigated showing that the growth rate is monotonously decreased if the transverse spread is increased. Nevertheless, the presence of ions generates that the instability can develop for significantly higher electron temperatures. Suppression of oblique mode is also explored by introducing a parallel velocity spread.

Gyrokinetic Simulations of Solar Wind Turbulence from Ion to Electron Scales

A three-dimensional, nonlinear gyrokinetic simulation of plasma turbulence resolving scales from the ion to electron gyroradius with a realistic mass ratio is presented, where all damping is provided by resolved physical mechanisms. The resulting energy spectra are quantitatively consistent with a magnetic power spectrum scaling of k(-2.8) as observed in in situ spacecraft measurements of the "dissipation range" of solar wind turbulence. Despite the strongly nonlinear nature of the turbulence, the linear kinetic Alfvén wave mode quantitatively describes the polarization of the turbulent fluctuations. The collisional ion heating is measured at subion-Larmor radius scales, which provides evidence of the ion entropy cascade in an electromagnetic turbulence simulation.

Non-stationarity of the quasi-perpendicular bow shock: comparison between Cluster observations and simulations

Abstract. We have performed full particle electromagnetic simulations of a quasi-perpendicular shock. The shock parameters have been chosen to be appropriate for the quasi-perpendicular Earth's bow shock observed by Cluster on 24 January 2001 (Lobzin et al., 2007). We have performed two simulations with different ion to electron mass ratio: run 1 with mi/me=1840 and run 2 with mi/me=100. In run 1 the growth rate of the modified two-stream instability (MTSI) is large enough to get excited during the reflection and upstream gyration of part of the incident solar wind ions. The waves due to the MTSI are on the whistler mode branch and have downstream directed phase velocities in the shock frame. The Poynting flux (and wave group velocity) far upstream in the foot is also directed in the downstream direction. However, in the density and magnetic field compression region of the overshoot the waves are refracted and the Poynting flux in the shock frame is directed upstream. The MTSI is suppressed in the low mass ratio run 2. The low mass ratio run shows more clearly the non-stationarity of the shock with a larger time scale of the order of an inverse ion gyrofrequency (Ωci): the magnetic field profile flattens and steepens with a period of ~1.5Ωci−1. This non-stationarity is different from reformation seen in previous simulations of perpendicular or quasi-perpendicular shocks. Beginning with a sharp shock ramp the large electric field in the normal direction leads to high reflection rate of solar wind protons. As they propagate upstream, the ion bulk velocity decreases and the magnetic field increases in the foot, which results in a flattening of the magnetic field profile and in a decrease of the normal electric field. Subsequently the reflection rate decreases and the whole shock profile steepens again. Superimposed on this 'breathing' behavior are in the realistic mass ratio case the waves due to the MTSI. The simulations lead us to a re-interpretation of the 24 January 2001 bow shock observations reported by Lobzin et al. (2007). It is suggested that the high frequency waves observed in the magnetic field data are due to the MTSI and are not related to a nonlinear phase standing whistler. Different profiles at the different spacecraft are due to the non-stationary behavior on the larger time scale.

Electron Current Drive by Fusion-Product-Excited Lower Hybrid Drift Instability

We present first principles simulations of the direct collisionless coupling of the free energy of fusion-born ions into electron current in a magnetically confined fusion plasma. These simulations demonstrate, for the first time, a key building block of some "alpha channeling" scenarios for tokamak experiments. Spontaneously excited obliquely propagating waves in the lower hybrid frequency range undergo Landau damping on resonant electrons, drawing out an asymmetric tail in the electron parallel velocity distribution, which carries a current.

Dependence of anomalous resistivity on bulk drift velocity of electrons in the reconnecting current sheets in solar flares

Anomalous resistivity is critical for triggering fast magnetic reconnection in the nearly collisionless coronal plasma. Its nonlinear dependence on bulk drift velocity is usually assumed in MHD simulations. However, the mechanism for the production of anomalous resistivity and its evolution is still an open question. We numerically solved the one dimension Vlasov equation with the typical solar coronal parameters and realistic mass ratios to infer the relationship between anomalous resistivity and bulk drift velocity of electrons in the reconnecting current sheets as well as its nonlinear characteristics. Our principal findings are summarized as follows: 1) the relationship between the anomalous resistivity and bulk drift velocity of electrons relative to ions may be described as Ωm for vd/ve in the range of 1.4–2.0 and Ωm for vd/ve in the range of 2.5–4.5; 2) if drift velocity is just slightly larger than the threshold of ion-acoustic instability, the anomalous resistivity due to the wave-particle interactions is enhanced by about five orders as compared with classic resistivity due to Coulomb collisions. With the increase of drift velocity from 1.4ve to 4.5ve, the anomalous resistivity continues to increase 100 times; 3) in the rise phase of unstable waves, the anomalous resistivity has the same order as the one estimated from quasi-linear theory; after saturation of unstable waves, the anomalous resistivity decreases at least about one order as compared with its peak value; 4) considering that the final velocity of electrons ejected out of the reconnecting current sheet (RCS) decreases with the distance from the neutral point in the neutral plane, the anomalous resistivity decreases with the distance from the neutral point, which is favorable for the Petschek-like reconnection to take place.

DEPENDENCE OF THE ANOMALOUS RESISTIVITY ON THE INDUCED ELECTRIC FIELD IN SOLAR FLARES

Anomalous resistivity is a critical parameter for triggering the fast magnetic reconnection and interpreting the eruption of solar flares in the nearly collisionless coronal plasma. However, the mechanism for the production of anomalous resistivity and its evolution are weakly understood. In this paper, the one-dimensional Vlasov equation was numerically solved with the typical solar coronal parameters and realistic mass ratio in the presence of strong inductive electric field, and the relationship between the anomalous resistivity and the reconnecting electric field was inferred for the area near the center of reconnecting current sheets. Our principal findings are summarized as follows. (1) The relationship between the anomalous resistivity and the reconnecting electric field E 0 may be represented by ηeff = [10.82-10.99 exp (–0.36 E 0)]Ω m. (2) If E 0 is small enough, it may be described by ηeff = [4.02 E 0 – 0.18]Ω m, which is basically consistent with the early experimental results on the plasma response to the applied electric field. (3) In comparison with theoretical formulas for the current-driven ion-acoustic and Buneman anomalous resistivities, if E 0 is small, the anomalous resistivity may be due to the ion-acoustic instability; if E 0 is large, the anomalous resistivity may be due to the Buneman instability. These results are also basically consistent with early experiments.

Particle-in-cell and hypernetted chain models of two-component, two-temperature coupled classical plasmas

Three-dimensional simulations of moderately to strongly coupled electron-ion and multicomponent classical plasmas using the particle-in-cell method are presented. The simulations resolve sub-Debye-length interparticle spacing to accurately model the dynamics of these systems. We consider realistic mass ratios and quasiequilibrium conditions with different component temperatures which are relevant on short time scales. The simulation results are in very good agreement with classical hypernetted chain calculations for dense electron-ion and ion-ion plasmas. Our results demonstrate the feasibility and utility of large-scale particle-in-cell simulations for the modeling and analysis of multicomponent moderately and strongly coupled plasmas.

Two-dimensional fully kinetic simulations of driven magnetic reconnection with boundary conditions relevant to the Magnetic Reconnection Experiment

Two-dimensional fully kinetic simulations are performed using global boundary conditions relevant to model the Magnetic Reconnection Experiment (MRX) [M. Yamada et al., Phys Plasmas 4, 1936 (1997)]. The geometry is scaled in terms of the ion kinetic scales in the experiment, and a reconnection layer is created by reducing the toroidal current in the flux cores in a manner similar to the actual experiment. The ion-scale features in these kinetic simulations are in remarkable agreement with those observed in MRX, including the reconnection inflow rate and quadrupole field structure. In contrast, there are significant discrepancies in the simulated structure of the electron layer that remain unexplained. In particular, the measured thickness of the electron layers is 3–5 times thicker in MRX than in the kinetic simulations. The layer length is highly sensitive to downstream boundary conditions as well as the time over which the simulation is driven. However, for a fixed set of chosen boundary conditions, an extrapolation of the scaling with the ion to electron mass ratio implies that at realistic mass ratio both the length and width will be too small compared to the experiment. This discrepancy implies that the basic electron layer physics may differ significantly between MRX and the two-dimensional, collisionless simulations. The two leading possibilities to explain the discrepancy are weak Coulomb collisions and three-dimensional effects that are present in the experiment but not included in the simulation model.

A particle simulation of current sheet instabilities under finite guide field

The instability of a Harris current sheet under a broad range of finite guide field (BG) is investigated using a linearized (δf) gyrokinetic electron and fully kinetic ion particle simulation code. The simulation is carried out in the two-dimensional plane containing the guide field along y and the current sheet normal along z. In this particle model, the rapid electron cyclotron motion is removed, while the realistic mass ratio mi∕me, finite electron Larmor radii, and wave-particle interactions are kept. It is found that for a finite BG∕Bx0⩽1, where Bx0 is the asymptotic antiparallel component of magnetic field, three unstable modes, i.e., modes A, B, and C, can be excited in the current sheet. Modes A and C, appearing to be quasielectrostatic modified two-stream instability/whistler mode, are located mainly on the edge of the current sheet. Mode B, on the other hand, is confined in the current sheet center and carries a compressional magnetic field (δBy) perturbation along the direction of electron drift velocity. Our new finding suggests that mode B may contribute directly to the electron anomalous resistivity in magnetic reconnection. In the cases with extremely large BG∕Bx0⪢1, the wave modes evolve to a globally propagating instability. The simulation shows that the presence of finite BG modifies the physics of the current sheet significantly.

A minimal model of parallel electric field generation in a transversely inhomogeneous plasma

AbstractThe generation of parallel electric fields by the propagation of ion cyclotron waves (with frequency 0.3 ωci) in the plasma with a transverse density inhomogeneity was studied. Using two-fluid, cold plasma linearised equations, it was shown for the first time that, in this particular context, E∥ generation can be understood by an analytic equation that couples E∥ to the transverse electric field of the driving ion cyclotron wave. It was proven that the minimal model required to reproduce the previous kinetic simulation results of E∥ generation [Tsiklauri et al 2005, Génot et al 2004] is the two-fluid, cold plasma approximation in the linear regime. By considering the numerical solutions it was also shown that the cause of E∥ generation is the electron and ion flow separation induced by the transverse density inhomogeneity. We also investigate how E∥ generation is affected by the mass ratio and found that amplitude attained by E∥ decreases linearly as inverse of the mass ratio mi/me. For realistic mass ratio of mi/me=1836, such empirical scaling law, within a time corresponding to 3 periods of the driving ion cyclotron wave, is producing E∥=14 Vm−1 for solar coronal parameters. Increase in mass ratio does not have any effect on final parallel (magnetic field aligned) speed attained by electrons. However, parallel ion velocity decreases linearly with inverse of the mass ratio mi/me. These results can be interpreted as following: (i) ion dynamics plays no role in the E∥ generation; (ii) E∥ ∝ 1/mi scaling is caused by the fact that ωd = 0.3 ωci ∝ 1/mi is decreasing with the increase of ion mass, and hence the electron fluid can effectively “short-circuit” (recombine with) the slowly oscillating ions, hence producing smaller E∥.

A minimal model of parallel electric field generation in a transversely inhomogeneous plasma

We study the generation of parallel electric fields by virtue of propagation of ion-cyclotron (IC) waves (with frequency 0.3 ωci) in the plasma with a transverse density inhomogeneity. Using two-fluid, cold plasma linearized equations, we show for the first time that E∥ generation can be understood by an analytic equation that couples E∥ to the transverse electric field of the driving IC wave. We prove that the minimal model required to reproduce previous kinetic results on E∥ generation is the two-fluid, cold plasma approximation in the linear regime. In this simplified model, the generated E∥ amplitude e.g. for plausible solar coronal parameters attains values of ≈90 V m−1 for the mass ratio mi/me = 262, within a time corresponding to three periods of the driving IC wave. By considering the numerical solutions we also show that the cause of E∥ generation is electron and ion flow separation (which is not the same as electrostatic charge separation) induced by the transverse density inhomogeneity. The model also correctly reproduces the previous kinetic results in that only electrons are accelerated (along the background magnetic field), while ions do not accelerate substantially. We also investigate how E∥ generation is affected by the mass ratio and find that amplitude attained by E∥ decreases linearly as the inverse of the mass ratio mi/me, i.e. E∥ ∝ 1/mi. This result contradicts the earlier suggestion by Génot et al (1999 J. Geophys. Res. 104 22649; 2004 Ann. Geophys. 6 2081) that the cause of E∥ generation is the polarization drift of the driving wave, which scales as ∝mi. Also, for a realistic mass ratio of mi/me = 1836 our empirical scaling law produces E∥ = 14 V m−1 (for solar coronal parameters). Increase in mass ratio does not have any effect on the final parallel (magnetic field aligned) speed attained by electrons. However, parallel ion velocity decreases linearly with the inverse of the mass ratio mi/me, i.e. the parallel velocity ratio of electrons and ions scales directly as mi/me. These results can be interpreted as follows: (i) ion dynamics plays no role in the E∥ generation; (ii) decrease in the generated parallel electric field amplitude with the increase of the mass ratio mi/me is caused by the fact that is decreasing, and hence the electron fluid can effectively ‘short-circuit’ (recombine with) the slowly oscillating ions, hence producing smaller E∥ which also scales exactly as 1/mi.