Electromagnetic Proton Cyclotron Instability Research Articles

Role of nonthermal solar wind protons in the excitation of electromagnetic proton-cyclotron instability: a kinetic theory based exact numerical investigation

Free transverse kinetic energy i.e. perpendicular temperature anisotropy of protons excite the electromagnetic ion/proton cyclotron instability which is pertained to waves associated with prevalent electromagnetic ion/proton cyclotron emissions in various natural regions of plasmas. The transverse dielectric response function of left hand circularly polarized electromagnetic proton cyclotron (EPC) instability is calculated for two models of nonthermal Cairns distributed plasmas. These models are distinguished according to the effective thermal velocities of protons. For the energetic nonthermal protons populations, nonthermality dependent effective temperature model is proposed which significantly contributes in the excitation of aforementioned plasma mode and cause an appreciable enhancement in the instability growth rate. Exact numerical solution of dispersion relation yields oscillatory real frequency and growth rate of instability. A comparative analysis is also carried out to examine the instability behavior in distinct nonthermal and thermal plasma models. Contemporary numerical investigations are highly beneficial to understand the intricate dynamics of space plasmas.

Pickup proton instabilities and scattering in the distant solar wind and the outer heliosheath: Hybrid simulations

The growth of magnetic field fluctuations driven by the injection of pickup ions perpendicular to a background magnetic field in a homogeneous, collisionless plasma is studied using one‐dimensional hybrid simulations. Freshly ionized protons are continuously injected into the simulations at constant rates and relative speeds consistent with conditions in the distant solar wind and the outer heliosheath. The pickup protons initially form a ring‐velocity distribution unstable to the electromagnetic proton cyclotron instability and lead to enhanced magnetic fluctuations. After an exponential growth phase of the instability, the fluctuating magnetic fields exhibit linear temporal growth followed by a more‐slowly growing quasi‐steady phase. The excited fluctuations pitch angle scatter the pickup protons toward an isotropic shell velocity distribution with the most significant scattering occurring in the exponential growth phase. The scattering rate of the freshly injected pickup protons during the linear temporal growth phase remains relatively constant and it increases with the pickup proton injection rate. More importantly, significant pitch angle scattering only occurs after the accumulated pickup proton density exceeds a critical value, the scattering‐onset density. The scattering‐onset density also increases with the pickup proton injection rate and the scattering onset typically occurs during the exponential growth phase of the magnetic fluctuations. Scaling relations for the scattering rate and the scattering‐onset density versus the pickup proton injection rate are derived from the simulation results. These relations suggest that significant scattering of pickup protons in the outer heliosheath occurs in a relatively limited spatial range close to the heliopause, related to the issue of whether the “secondary ENA” mechanism is a possible explanation for the ENA ribbon observed by IBEX. Implications of the results on pickup proton dynamics in the distant solar wind are also discussed.

A study of the electromagnetic proton cyclotron instability as a generation mechanism for EMIC waves in the Earth's magnetosphere using SCATHA data

Using 59 days of magnetic field data from SCATHA, a study of the electromagnetic proton cyclotron instability as a generation mechanism for EMIC waves in the Earth's magnetosphere has been conducted. From 1181 events found, we selected 373 events that were not influenced by the presence of He+ and O+ ions, i.e., events with frequency above the local He+ cyclotron frequency and that had all the required accompanying data. These events occurred in all magnetic local times (MLT) sectors, with L ranging from 5.6 to 8.1 and magnetic latitudes (MLAT) from −13.7° to 15.6°. Assuming a pure proton plasma, the proton temperature anisotropy, Ap, is determined from the maximum normalized frequency at which power is emitted. Using measured parameters and estimated total number density, the convective growth rate, S, of Electromagnetic Ion Cyclotron (EMIC) waves as a function of frequency depends only on the parallel proton temperature, T∥. Matching the observed peak in the frequency spectrum and the calculated peak in S allows the determination of T∥ and the proton perpendicular temperature, T⊥, for each event. Analysis of the results yields a new empirical expression for Ap as a function of the hot proton parallel beta, β∥h, and the maximum value of the wave temporal growth rate. The relationship between Ap and β∥h is consistent with theoretical predictions. The dependence of Ap on T∥ is consistent with the expectation that the free energy source of EMIC waves is energetic protons with T⊥ > T∥.

Signatures of wave‐ion interactions in the solar wind: Ulysses observations

Theory and simulations predict that resonant wave‐particle scattering by enhanced magnetic fluctuations yields characteristic signatures in properties of solar wind ions. Here Ulysses/Solar Wind Observations Over the Poles of the Sun (SWOOPS) instrument measurements of protons and alpha particles are examined to seek three types of these signatures: (1) a statistical constraint on the proton temperature anisotropy imposed by the electromagnetic proton cyclotron instability; (2) a correlation between the alpha anisotropy and the alpha/proton relative flow speed driven by electromagnetic alpha/proton instabilities; and (3) relationships among the proton anisotropy, the alpha anisotropy, and the alpha/proton speed induced by the cascade of long‐wavelength Alfvén fluctuations to ion cyclotron resonances at shorter wavelengths. No signatures of alpha/proton instabilities are found. However, the first example of the proton anisotropy constraint in the slow solar wind is demonstrated, and a theoretical prediction for Alfvén/cyclotron wave acceleration in the fast wind is similar to a statistical lower bound observed on the alpha/proton speed.

Electromagnetic proton cyclotron anisotropy instability: Wave‐particle scattering rate

The electromagnetic proton cyclotron instability is driven by a proton temperature anisotropy T⟂p/T∥p>1 where the directional subscripts denote directions relative to the background magnetic field. Enhanced field fluctuations from instability growth lead to wave‐particle scattering which reduces the anisotropy; previous research has demonstrated that the anisotropy is constrained by a power‐law function of β∥p. Here two‐dimensional hybrid simulations in a homogeneous, magnetized, collisionless plasma are used to derive a scaling relation for the maximum scattering rate of proton anisotropy reduction. The result is a function only of the anisotropy and β∥p and so is appropriate for use in fluid models of anisotropic plasmas such as the magnetosheath.

Survey of pancake‐shaped warm ion distributions at geosynchronous orbit

It has been proposed that the electromagnetic proton cyclotron instability is a strong source of heating for the anisotropic warm ions observed at geosynchronous orbit. We present here the results of a statistical study of pancake‐shaped warm ion distributions using a 1‐year interval of data observed with the Los Alamos magnetospheric plasma analyzer on the geosynchronous satellite 1994–084. Our results support previous findings that pancake‐shaped warm ion distributions occur more frequently on the dayside of the magnetosphere and occur very close to the plasmapause. We also confirm that the electromagnetic proton cyclotron instability is operating and is constraining the hot proton temperature anisotropy. However, our results indicate that the pancake‐shaped warm ion distributions observed at geosynchronous orbit are probably not generated by this instability but must be due to a different mechanism, possibly heating by lower hybrid waves.

Proton temperature anisotropy upper bound

The electromagnetic proton cyclotron instability and the mirror instability are driven by the proton temperature anisotropy T⊥p/T‖p > 1, where ⊥ and ‖ denote directions relative to the background magnetic field. Linear theory and one‐dimensional hybrid simulations imply that the former mode grows more rapidly over 0.05 ≤ β‖p ≤ 5 and that wave‐particle scattering by its enhanced fluctuations imposes an upper bound on the temperature anisotropy of the form urn:x-wiley:01480227:media:jgra13669:jgra13669-math-0001 where and B0 is the background magnetic field. Here Sp and αp are fitting parameters, and . This paper describes results from more general two‐dimensional hybrid simulations, which permit both instabilities to grow simultaneously. These simulations confirm the one‐dimensional results on the initial domain ; enhanced fluctuations display the properties of the proton cyclotron instability and αp ≃ 0.4. On this domain the two‐dimensional simulations also yield an upper bound for the fluctuating field energy density of the form urn:x-wiley:01480227:media:jgra13669:jgra13669-math-0005 with fitting parameter . The simulations on the initial domain 10 ≤ β‖p≤100 show spectral characteristics of both instabilities and exhibit a more stringent bound on the proton anisotropy, in agreement with observations in the terrestrial magnetosheath.

Warm protons at geosynchronous orbit

Ions in the outer magnetosphere typically are observed to consist of a hot (T ∼ 10 keV) component and a cool constituent with energies of a few eV. The hot component often is observed to be anisotropic with T⊥ > T‖, where the subscripts denote directions relative to the background magnetic field, whereas the cool ions exhibit a wide variety of anisotropies. The Los Alamos magnetospheric plasma analyzer (MPA) instruments measure ion and electron velocity distributions from about 1 eV to about 40 keV at geosynchronous orbit. In the afternoon and evening sectors MPA observations show that cool ions, which are assumed to be protons, are sometimes “warm” with temperatures of order 10 eV and T⊥ > T‖. Theory and simulations of the electromagnetic proton cyclotron instability, which is driven by the hot proton anisotropy, have shown that the resulting enhanced field fluctuations heat initially cool protons. Moreover, this process implies a scaling relation for the apparent temperature of the warm protons as a function of the relative densities of the two components. This manuscript describes an examination of MPA data which shows that this scaling relation provides an approximate upper bound for a selected set of warm proton temperatures observed at geosynchronous orbit. This result is consistent with the hypothesis that the proton cyclotron instability is an important energization source for warm protons at geosynchronous orbit.

Proton temperature anisotropy in the magnetosheath: Hybrid simulations

Scattering by enhanced fluctuations from the electromagnetic proton cyclotron instability imposes an upper bound on the proton temperature anisotropy of the form T⟂p/T∥p −1 = Sp/β∥pαp. Here β∥p is the proton β based on T∥p and the directional subscripts indicate directions perpendicular and parallel to the background magnetic field. This paper describes the analysis of the proton temperature anisotropy in two‐dimensional hybrid simulations of quasi‐perpendicular shocks and their associated magnetosheaths. Three simulations are considered: at low, intermediate, and high upstream Mach numbers. Considering results from well downstream of all three shocks as one data set, an upper bound on the proton temperature anisotropy fits the above equation with αp=0.5. This compares favorably to αp values from other simulations and from sheath observations.

Electromagnetic proton cyclotron instability: Interactions with magnetospheric protons

The temperature anisotropy of the hot (keV) protons of the outer magnetosphere can excite the electromagnetic proton cyclotron instability. Wave‐particle scattering by this instability not only maintains the hot proton anisotropy at or below an upper bound but also imparts energy to the cool (eV) proton component. This instability and its consequences are examined through the use of linear and second‐order Vlasov theory and one‐dimensional hybrid simulations in a homogeneous plasma model which represents these two protonic constituents. A different form for the upper bound on the hot proton anisotropy is derived from linear theory and the simulations; comparison against plasma observations from Los Alamos magnetospheric plasma analyzers in geosynchronous orbit shows very good agreement. Second‐order theory and simulations are used to obtain a different scaling for the late‐time apparent temperature of the cool proton component Tc which indicates that it is inversely correlated with the cool proton density nc. Observations in both the plasmasphere and the outer magnetosphere sometimes show a similar inverse correlation, suggesting that the electromagnetic proton cyclotron instability is an important contributor to cool proton heating in these regions.

Comparative study of the effect of cold ions and thermal anisotropy on the convective electromagnetic proton cyclotron instability

Although the role played by cold ions on the electromagnetic proton-cyclotron instability has been thoroughly investigated, there are some aspects which deserve further attention. Moreover, since the presence of ion cyclotron waves in the magnetosphere has been experimentally established it is important to have a full understanding of the role played by cold ions. Thus, it is shown here that the main effect of cold ions on the proton-cyclotron instability is to shift the unstable spectrum. If the only cold species are protons, then the shift of the spectrum is always towards lower frequency values, i.e. away from the marginal mode. If in the absence of cold protons the maximum convective growth rate lies far from the marginal mode, the only effect of cold protons is to shift the spectrum further away from the marginal mode. However, if the maximum convective growth rate in the absence of cold protons lies close to the marginal mode, then the shift of the spectrum leads also to a large amplification. The reason for this behaviour lies in the fact that as the thermal anisotropy decreases, the frequency range of the unstable spectrum also decreases, stabilizing high frequency waves. Since unstable higher frequency waves occur in the absence of cold protons, these are the first to be stabilized. The observed amplification due to cold protons is the result of comparing waves which have suffered some stabilization with waves which, due to the shift of the unstable spectrum, have not yet been affected by the stabilization which follows the reduction of the thermal anisotropy. A consequence of these results is that, since the thermal anisotropy decreases as the instability develops, the instability lasts longer in the presence of cold protons than in their absence. If more than one cold species are present, the situation is more complex but the basic mechanism is the same. It is conjectured that the catalytic role played by cold He + ions in the generation of ion cyclotron waves in the magnetosphere consists of shifting the unstable spectrum away from a forbidden or sta- bilization region.

Modifications in the maximum convective growth rate of the electromagnetic proton cyclotron instability due to the presence of thermal ions

The effect of thermal ions on the convective properties of the electromagnetic proton cyclotron instability is investigated. It is shown that when Ap < 1, where Ap is the proton anisotropy, cold ions, with relative specific charge mj/Zj mp ≥ 1, stabilize the convective growth of the instability. When Ap >1, the effect of thermal ions is to enhance the convective growth of the instabifity in the range where the real part of the frequency, ωr, is smaller than the ion gyrofrequency, Ωj. The maximum enhancement, corresponding to an optimum concentration of heavy ions, is shown to be a constant independent of the species. However, for each species, even for Ap > 1 (except for protons), there is always a range of values of Ap such that the species will stabilize the system. Heavier ions are shown to be more effective in enhancing the convective growth of the instability, in the sense that, the heavier they are, smaller relative concentrations are required to reach the constant value mentioned above. For sufficiently heavy species, the required concentration to optimize the convective growth, is independent of the species.

Requirements on singly ionized lithium concentrations for magnetospheric seeding experiments

Optimum concentrations of singly ionized Li relative to warm protons, η ≡ nLi/np,w, for magnetospheric seeding experiments aimed at enhancing the electromagnetic proton cyclotron instability have been obtained analytically and numerically. This has been done by calculating the absolute maximum growth rates γmaxabs and enhancement F ≡ γmaxabs/γmax(η = 0) for the proton instability branch upon addition of cold lithium ions to an infinite anisotropic proton plasma. A necessary condition for enhancement is P ≡ βpAp²(Ap + 1) ≪ 1, where βp ≡ 8πnpKT∥,p/B0² and Ap ≡ (T⊥/T∥)p − 1. The shape of the linearly unstable spectrum strongly depends on the parameter [Ap/(Ap + 1)]/(mLi/ZLimp)−1. When the condition stated above is satisfied, the growth rate and the extension of the unstable spectrum in k space may increase with η. An optimum η value is found to exist.