Bounce Resonance Research Articles

A toy model to explain the missing bounce windows in the kink-antikink collisions

We propose a toy model to reproduce the fractal structure of kink and antikink collisions on one topological sector of ϕ6 theory. Using the toy model, we investigate the missing bounce windows observed in the fractal structure, and show that the coupling between two oscillation modes modulate the emergence of the missing bounce windows. By numerical calculation, we present that the two bounce resonance corresponds to the lower eigenfrequency of the toy model.

Bounce Resonance Between Energetic Electrons and Magnetosonic Waves: A Parametric Study

AbstractMagnetosonic (MS) waves are electromagnetic emissions from a few to 100 Hz primarily confined near the magnetic equator both inside and outside the plasmasphere. Previous studies proved that MS waves can transport equatorially mirroring electrons from an equatorial pitch angle of 90° down to lower values by bounce resonance. However, the dependence of the bounce resonance effect on wave or background plasma parameters is still unclear. Here, we applied a test particle simulation to investigate electron transport coefficients, including diffusion and advection coefficients in energy and pitch angle, due to bounce resonance with MS waves. We investigate five wave field parameters, including wave frequency width, wave center frequency, latitudinal distribution width, wave normal angle root‐mean‐square of wave magnetic amplitude, and two background parameters, L‐shell value and plasma density. We find different transport coefficient peaks resulting from different bounce resonance harmonics. Higher‐order harmonic resonances exist, but the effect of fundamental resonance is much stronger. As the wave center frequency increases, higher‐order harmonics start to dominate. With wave frequency width increasing, the energy range of effective bounce resonance broadens, but the effect itself weakens. The bounce resonance effect will increase when we decrease the wave normal angle, or increase the wave amplitude, latitudinal distribution width, L‐shell value, and plasma density. The parametric study will advance our understanding of the favorable conditions of bounce resonance.

Effects of NBI-induced energetic ions on internal kink stability in HL-2M

A systematic investigation is carried out, studying the effect of the neutral beam injection induced energetic particles (EPs) on the n = 1 (n is the toroidal mode number) internal kink (IK) instability in the HL-2M tokamak, utilizing the MARS-F/K code [Liu et al., Phys. Plasmas 7, 3681 (2000) and 15, 112503 (2008)]. A high-beta sawteething HL-2M scenario, simulated by the TRANSP code [Breslau et al. Computer Software (2018)], is chosen for this study. Compared to the fluid model, non-perturbative magnetohydrodynamic (MHD)-kinetic hybrid computations with MARS-K show a generally stabilization effect on the IK, due to drift kinetic resonances associated with EPs. The bounce resonance of trapped EPs has minor influence on the mode stability. In the absence of the plasma equilibrium flow and with the assumed particle pitch distribution, the transit resonance of co-current (countercurrent) passing EPs destabilizes (stabilizes) the IK. With plasma flow, both co- and countercurrent passing EPs tend to stabilize the mode, but the effect is stronger with the countercurrent particles. These modeling results provide useful guidance for interpreting MHD instabilities in the future high-performance experiments in HL-2M.

Scale-invariant resonance characteristics in magnetized capacitive radio frequency plasmas

Resonance mechanisms have been found to be essential for the generation of high-density rf plasmas at low pressures, in which electrons can be continuously accelerated through multiple interactions with the oscillating rf sheaths. In this work, we report the scale-invariant resonance mechanisms, such as bounce resonance heating and plasma series resonance, in low-pressure capacitive rf plasmas in the presence of an external magnetic field. The generation conditions for the resonance mechanisms are determined via fully kinetic simulations. It is found that the resonance dynamical properties of single-frequency plasmas (e.g., a double-peak electron density vs magnetic field curve) can be exactly replicated at different scales when three combined control parameters, i.e., the reduced gap distance pd (pressure × distance), reduced driving frequency f/p (frequency divided by pressure), and reduced magnetic field B/p (magnetic field divided by pressure), are kept constant. The similarity relations for the electron density and electron power absorption in magnetized rf plasmas are numerically confirmed. Furthermore, the similarity and scale-invariant resonance characteristics are elucidated through the scaling of the Boltzmann equation with collisional terms for weakly ionized rf plasmas with a magnetic field, which is proven to be theoretically exact.

Numerical study on influences of parallel sonic wave damping, precession, and bounce resonances on resistive wall modes in CFETR

Adopting an 11 MA steady-state reversed magnetic shear equilibrium of the China Fusion Engineering Test Reactor, the influence of parallel sonic wave damping, precession, and bounce resonances on the resistive wall mode (RWM) at different plasma pressures and plasma toroidal rotations is numerically investigated using the MARS-K code. We find that the parallel sonic wave damping, precession, and bounce resonances have damping effects on the RWM. The RWM is stabilized by the parallel sonic wave damping at low plasma pressure. At the two q = 3 rational surfaces, the RWM is the most unstable, but the precession resonance mainly occurs at one of the q = 3 rational surfaces, so the RWM cannot be stabilized. In addition, the precession resonance and bounce resonance occur simultaneously, and there are two roots. One is the precession resonance root, and another is the bounce resonance root. The bounce resonance has a stabilizing effect on the RWM.

Modeling of thermal-ion-driven internal kink in DIII-D high-T i plasmas

Toroidal modeling utilizing the non-perturbative magnetohydrodynamic-kinetic hybrid code MARS-K (Liu Y.Q. et al 2008 Phys. Plasmas 15 112503), to a DIII-D high-performance discharge with the core thermal ion temperature of T i ∼ 13 keV, finds multiple branches of unstable internal kink (IK) modes triggered by the bounce resonance of trapped thermal ions. The range of the computed mode frequency aligns well with the bounce frequency of trapped thermal ions, confirming the nature of resonance drive for the instability. The computed mode frequency is close to that observed in experiments. Plasma toroidal flow, in particular the fast flow (10% of Alfvén speed) as in the considered DIII-D discharge, strongly stabilizes the fluid IK branch but not all of the thermal-ion-driven internal kink (TIK) branches, leaving one dominant unstable TIK branch under the experimental conditions. Plasma resistivity also significantly affects stability of the TIKs (but not much on the IK which is ideally strongly unstable) in combination with the drift kinetic drive by thermal ions. High resistivity can drive additional unstable TIK branches. Scanning the on-axis safety factor over a large range confirms robustness of the TIK triggering by thermal ions. The computed TIKs contain both the IK and the tearing components as the dominant contributions to the eigenmode structure. These findings, together with the experimental results reported in reference (Du X.D. et al 2021 Phys. Rev. Lett. 127 025001), strongly suggest the possibility of thermal-ion driven instabilities in ITER.

Effects of chamber size on electron bounce-resonance heating and power deposition profile in a finite inductive discharge

Effects of chamber size on electron bounce-resonance heating (BRH) and power deposition profile are numerically studied in a finite inductive Ar discharge under a low-pressure range of 0.3–3 Pa. The BRH characterized by a plateau formation in the electron energy probability function (EEPF) exists only at the small chamber radius and relatively low pressure and is enhanced at a larger chamber height. It is attributed to a remarkable increase in the energy diffusion coefficient caused by electron heating at the first bounce resonance condition. As increasing chamber radius and pressure, the enhancement in the energy diffusion coefficient caused by electron–electron collisions tends to Maxwellianize the EEPF, thus resulting in weakness and even disappearance of the BRH. For relatively low pressure, the number of positive and negative power deposition regions increases with increasing chamber radius, and there is no region of negative power deposition at the small chamber radius where the skin depth becomes closer to the chamber radius.

Magnetospheric response to solar wind forcing: ultra-low-frequency wave–particle interaction perspective

Abstract. Solar wind forcing, e.g., interplanetary shock and/or solar wind dynamic pressure pulses impacting Earth's magnetosphere, manifests many fundamental important space physics phenomena, including producing electromagnetic waves, plasma heating, and energetic particle acceleration. This paper summarizes our present understanding of the magnetospheric response to solar wind forcing in the aspects of radiation belt electrons, ring current ions and plasmaspheric plasma physics based on in situ spacecraft measurements, ground-based magnetometer data, magnetohydrodynamics (MHD) and kinetic simulations. Magnetosphere response to solar wind forcing is not just a “one-kick” scenario. It is found that after the impact of solar wind forcing on Earth's magnetosphere, plasma heating and energetic particle acceleration started nearly immediately and could last for a few hours. Even a small dynamic pressure change in interplanetary shock or solar wind pressure pulse can play a non-negligible role in magnetospheric physics. The impact leads to generation of a series of waves, including poloidal-mode ultra-low-frequency (ULF) waves. The fast acceleration of energetic electrons in the radiation belt and energetic ions in the ring current region response to the impact usually contains two contributing steps: (1) the initial adiabatic acceleration due to the magnetospheric compression, (2) followed by the wave–particle resonant acceleration dominated by global or localized poloidal ULF waves excited at various L-shells. Generalized theory of drift and drift–bounce resonance with growth- or decay-localized ULF waves has been developed to explain in situ spacecraft observations. The wave-related observational features like distorted energy spectrum, “boomerang” and “fishbone” pitch angle distributions of radiation belt electrons, ring current ions and plasmaspheric plasma can be explained in the framework of this generalized theory. It is worth pointing out here that poloidal ULF waves are much more efficient at accelerating and modulating electrons (fundamental mode) in the radiation belt and charged ions (second harmonic) in the ring current region. The results presented in this paper can be widely used in solar wind interacting with other planets such as Mercury, Jupiter, Saturn, Uranus and Neptune and other astrophysical objects with magnetic fields.

Bounce Resonance Scattering of Radiation Belt Energetic Electrons by Extremely Low‐Frequency Chorus Waves

AbstractBounce‐resonant diffusion coefficients of radiation belt energetic electrons induced by extremely low‐frequency (ELF) chorus waves are comprehensively evaluated using Van Allen Probes observations on December 22, 2014. ELF chorus waves can efficiently scatter 85° < eq < 89° electrons with bounce resonance pitch angle scattering rates above 10−4/s and energy scattering rates above 10−7/s. By comparing diffusion coefficients due to bounce resonance with those due to cyclotron and Landau resonances, we found that bounce resonance diffusion rates have slight energy dependence for >100 keV electrons while Landau‐resonant scattering rates decrease significantly in the MeV energy range. These findings suggest that bounce resonances by ELF chorus waves have potentially significant contributions to the dynamics of energetic electrons and should be considered in the further modeling of Earth's radiation belts.

Landau damping of electrons with bouncing motion in a radio-frequency plasma* *Project supported by the National Key Research and Development Program of China (Grant No. 2017YFE0300406) and the National Natural Science Foundation of China (Grant Nos. 11975272, 12075276, 11805133, 11705236, and 11375234).

One-dimensional particle simulations have been conducted to study the interaction between a radio-frequency electrostatic wave and electrons with bouncing motion. It is shown that bounce resonance heating can occur at the first few harmonics of the bounce frequency (nω b,n = 1,2,3,…). In the parameter regimes in which bounce resonance overlaps with Landau resonance, the higher harmonic bounce resonance may accelerate electrons at the velocity much lower than the wave phase velocity to Landau resonance region, enhancing Landau damping of the wave. Meanwhile, Landau resonance can increase the number of electrons in the lower harmonic bounce resonance region. Thus electrons can be efficiently heated. The result might be applicable for collisionless electron heating in low-temperature plasma discharges.

Excitation of fishbone-like mode in tokamaks due to bounce resonances of trapped thermal ions

When the drift kinetic effect of thermal ions is taken into account, a high-frequency fishbone-like mode (FLM) is found to be driven unstable by trapped thermal ions (TTIs) in tokamak plasmas, according to self-consistent magneto-hydrodynamic (MHD)-kinetic hybrid modeling utilizing the MARS-K code [Liu et al., Phys. Plasmas 15, 112503 (2008)] as well as an analytic theory. It is found that, similar to energetic particles, TTIs can also stabilize the internal kink mode, whereas the FLM is excited when the effective beta of TTIs exceeds a threshold value. The real frequency of the FLM is comparable to the bounce frequency of TTIs. The mode structure of the FLM can be significantly different from the conventional step-like function for the associated plasma radial displacement. This drift kinetic induced modification of the mode structure near the q = 1 surface is captured by non-perturbative MHD-kinetic hybrid computations with MARS-K. Furthermore, the FLM can only be triggered by TTIs at sufficiently high thermal temperatures. Both the FLM and the internal kink can be stabilized by sufficiently fast plasma toroidal rotation and parallel sound wave damping. These two conditions of high thermal temperature and (fast) flow stabilization, though making it challenging to observe the TTI-driven FLM in present day experiments, are favorable for the mode excitation in future reactor scale devices.

Study on electron stochastic motions in the magnetosonic wave field: Test particle simulations

Using the test particle simulation method, we investigate the stochastic motion of electrons with energy of 300 keV in a monochromatic magnetosonic (MS) wave field. This study is motivated by the violation of the quasi-linear theory assumption, when strong MS waves (amplitude up to ~1 nT) are present in the Earth’s magnetosphere. First, electron motion can become stochastic when the wave amplitude exceeds a certain threshold. If an electron initially resonates with the MS wave via bounce resonance, as the bounce resonance order increases, the amplitude threshold of electron stochastic motion increases until it reaches the peak at about the 11th order in our study, then the amplitude threshold slowly declines. Further, we find that the coexistence of bounce and Landau resonances between electrons and MS waves will significantly reduce the amplitude threshold. In some cases, the electron motion can become stochastic in the field of an MS wave with amplitudes below 1 nT. Regardless, if neither the bounce nor Landau resonance condition is satisfied initially, then the amplitude threshold of stochastic motion shows an increasing trend for lower frequencies and a decreasing trend for higher frequencies, even though the amplitude threshold is always very large (> 5 nT). Our study suggests that electron stochastic motion should also be considered when modeling electron dynamics regulated by intense MS waves in the Earth’s magnetosphere.

Excitation of Internally Driven ULF Waves by the Drift‐Bounce Resonance With Ring Current Ions Based on the Drift‐Kinetic Simulation

AbstractWe investigated the excitation mechanism and global distribution of internally driven Pc3‐Pc5 ultralow‐frequency waves in the inner magnetosphere using a kinetic and self‐consistent simulation (Geospace Environment Modeling System for Integrated Studies‐Ring Current model). These waves can be excited through the drift‐bounce resonance with ring current ions injected into the inner magnetosphere during substorms. Initial phase space density of ring current ions is the butterfly‐like distribution with the asymmetry in pitch angle direction. We find two kinds of internally driven ultralow‐frequency waves. First, the dynamic power spectra of the field fluctuations show the excitation of poloidal, toroidal, and compressional Pc5 waves. We find that the excited waves are fundamental modes propagating westward with the azimuthal wave number of m ~ − 50. These waves are excited by the drift resonance with ions having the energy of 50–150 keV. Second, we can reproduce the excitation of poloidal Pc3 waves in the dusk region with m ~ − 30, which are driven by the bounce resonance with ions having energies of 20–50 keV for the first time. We investigate the energy transfer between ions and waves and find that poloidal Pc5 and Pc3 waves are excited mainly by positive energy gradient of the phase space density, while we find the inward gradient of the phase space density at L > 6. The velocity distribution of the growth rate suggests that Pc5 waves are driven by ions with pitch angle of around 90°, while Pc3 waves are excited by ions at oblique pitch angle.

Excitation of Oxygen Ion Cyclotron Harmonic Waves in the Inner Magnetosphere: Hybrid Simulations

AbstractHybrid simulations are carried out to investigate the excitation of oxygen ion cyclotron harmonic waves observed in the inner magnetosphere. The simulations show that these waves can be excited by energetic oxygen ions of a ring‐like velocity distribution. The excited waves have properties consistent with observations, but their nearly perpendicular propagation disagrees with the quasi‐parallel propagation from the singular value decomposition (SVD) analysis reported earlier. By performing the same SVD analysis on the simulated waves in a three‐dimensional simulation, it is demonstrated that the superposition of multiple waves with different azimuthal angles can cause the commonly used SVD analysis of wave propagation to yield incorrectly small wave normal angles. In addition, the results show that the enhanced waves scatter oxygen ions mainly along v⊥ through cyclotron resonance. The waves may also scatter energetic radiation belt electrons through bounce resonance and transit time scattering, similar to fast magnetosonic waves.

Parametric Dependence of the Formation of Electron Butterfly Pitch Angle Distribution Driven by Magnetosonic Waves

AbstractUsing the full relativistic test particle (TP) simulation code, we investigate the parametric dependence of electron scattering and phase space density evolution driven by magnetosonic (MS) waves at L = 4.5 both inside and outside the plasmapause. The scattering effects caused by Landau resonance, bounce resonance, and the transit‐time effect are all involved in the study. The net scattering effects are evaluated in the form of diffusion coefficients with different combinations of MS wave parameters, such as frequency bandwidth and wave normal angle, and ambient plasma density. The results demonstrate that (1) Landau resonance and the transit‐time effect dominate the electron scattering inside and outside the plasmapause, respectively, while both are modulated by bounce resonant scattering; (2) bounce resonant scattering becomes more important with narrowband MS waves; (3) electron scattering induced by MS waves is highly sensitive to wave normal angle. The temporal phase space density (PSD) evolution obtained from 2‐D kinetic Fokker‐Planck simulations shows that MS waves with larger wave normal angles are more likely to generate electron butterfly pitch angle distributions (PADs) for hundreds of keV electrons outside the plasmapause. Our study suggests that the electron butterfly distribution has important implications for revealing the combined scattering of MS wave‐particle interactions, and the combination of the multiple scattering mechanisms should be carefully incorporated in future global modeling of radiation belt dynamics.

Fishbone instability driven by trapped fast ions in a toroidal plasma with reversed magnetic shear

Based on the non-perturbative approach, the hybrid code MARS-K is applied to study fishbone (FB) instabilities driven by trapped fast ions in a toroidal plasma with q profile nearly being flat or non-monotonic. We explore the dependency of the FB with variation in the fast ion distribution, thermal particle kinetic effects, safety factor (q) profile and plasma resistivity. When the safety factor minimum value is larger than unity (i.e. ), the mode can be excited by isotropic or anisotropic fast ions, with the latter strongly enhancing the mode growth rate. The mode frequency increases with increasing , and is more easily triggered in a equilibrium with two q = 1 surfaces, compared with the case with one or no q = 1 surface. Kinetic contributions from transit resonance of passing fast ions and from bounce resonance of trapped fast ions strongly enhance mode instability. The passing thermal ions induced Landau damping has a strong stabilization effect. Furthermore, in such a weak, even reversed magnetic shear plasma, the radial mode structure of FB mode monotonically decreases to zero at q = 1 flux surface instead of a step-like function, and it depends on the kinetic contributions from particles. In addition, the plasma resistivity significantly stabilizes the mode near the marginally unstable point.

Combined Scattering of Radiation Belt Electrons by Low‐Frequency Hiss: Cyclotron, Landau, and Bounce Resonances

AbstractLow‐frequency hiss is known to play an important role in the precipitation of radiation belt electrons by cyclotron, Landau, and bounce resonances. To investigate the potential combined scattering effect caused by these resonant processes, we analyze the resonant conditions and develop a full relativistic test particle code to quantify the net pitch angle scattering efficiency. It is indicated that the three resonance processes can coexist to scatter electrons at different energies and pitch angles, with the net pitch angle scattering rates up to ~10−3 s−1 for low‐frequency hiss ~175 pT at L = 4.5. Comparisons with the quasi‐linear theory results demonstrate that the cyclotron resonance is mainly responsible for the pitch angle scattering of electrons < ~ 80°, while both Landau and bounce resonances can affect the scattering of near‐equatorially mirroring electrons and their combined diffusion produces smaller scattering coefficients compared to quasi‐linear theory calculations.

Combined Scattering of Radiation Belt Electrons Caused by Landau and Bounce Resonant Interactions With Magnetosonic Waves

AbstractWe develop a full relativistic test particle code to model the combined electron scattering effect of Landau and bounce resonances with magnetosonic waves. Test particle simulations of magnetosonic wave‐electron interactions indicate that the two resonances coexist to affect radiation belt electrons at different energies and pitch angles, and the resultant combined pitch angle scattering and energy diffusion can reach the rates of ~10−4 and ~10‐5 s, respectively, for electrons ~40–500 keV at pitch angles ~ 70 ° – 80° for the given wave model (~200 pT) inside the plasmapause at L = 4.5. Comparisons with the quasi‐linear theory results show that the test particle combined scattering rates are generally an order of magnitude weaker, possibly because the electrons are moved out of the Landau resonance by the advective effect of the bounce resonance. Our investigation demonstrates that the Landau and bounce resonances with magnetosonic waves cannot be treated independently or additively in terms of quasi‐linear theory to simulate the associated radiation belt electron dynamics.

Feasibility Study of Wafer-Level Backside Process for InP-Based ICs

This paper reports wafer-level backside process technology, established with the intent to ensure stable operation of InP ICs in the submillimeter wavelength band, which generally suffer from ground bounce and substrate resonance. Our process consists of thinning a 3-in InP wafer, forming dense vias with interval cooling steps, backside metallization with single-level wiring and crack-free dicing. We investigate the effects of the backside process on InP-based heterojunction bipolar transistors and high electron mobility transistors. The results show that the backside process contributes to stable operation up to the 300-GHz range without any degradation of transistor characteristics.

Effect of Low‐Harmonic Magnetosonic Waves on the Radiation Belt Electrons Inside the Plasmasphere

AbstractIn this paper, we presented two observational cases and simulations to indicate the relationship between the formation of butterfly‐like electron pitch angle distributions and the emission of low‐harmonic (LH) fast magnetosonic (MS) waves inside the high‐density plasmasphere. In the wave emission region, the pitch angle of relativistic (>1 MeV) electrons becomes obvious butterfly‐like distributions for both events (near‐equatorially mirroring electrons are transported to lower pitch angles). Unlike relativistic (>1 MeV) electrons, energetic electrons (<1 MeV) change slightly, except that relatively low‐energy electrons (<~150 keV) show butterfly‐like distributions in the 21 August 2013 event. In theory, the LH MS waves can affect different‐energy electrons through the bounce resonance, Landau resonance, and transit time scattering. By performing the Fokker‐Planck diffusion simulations, we demonstrate that the bounce resonance with the LH MS waves mainly leads to the butterfly pitch angle distribution of MeV electrons, whereas the Landau resonance and transit time scattering mainly affect energetic electrons in the high‐density region.