Proton Heating Research Articles

Simultaneous Proton and Electron Energization during Macroscale Magnetic Reconnection

The results of simulations of magnetic reconnection accompanied by electron and proton heating and energization in a macroscale system are presented. Both species form extended power-law distributions that extend nearly three decades in energy. The primary drive mechanism for the production of these nonthermal particles is Fermi reflection within evolving and coalescing magnetic flux ropes. While the power-law indices of the two species are comparable, the protons overall gain more energy than electrons, and their power law extends to higher energy. The power laws roll into a hot thermal distribution at low energy with the transition energy occurring at lower energy for electrons compared with protons. A strong guide field diminishes the production of nonthermal particles by reducing the Fermi drive mechanism. In solar flares, proton power laws should extend down to tens of keV, far below the energies that can be directly probed via gamma-ray emission. Thus, protons should carry much more of the released magnetic energy than expected from direct observations.

Plasma Motions and Compressive Wave Energetics in the Solar Corona and Solar Wind from Radio Wave Scattering Observations

Radio signals propagating via the solar corona and solar wind are significantly affected by compressive waves, impacting the properties of solar bursts as well as sources viewed through the turbulent solar atmosphere. While static fluctuations scatter radio waves elastically, moving, turbulent, or oscillating density irregularities act to broaden the frequency of the scattered waves. Using a new anisotropic density fluctuation model from the kinetic scattering theory for solar radio bursts, we deduce the plasma velocities required to explain observations of spacecraft signal frequency broadening. The inferred velocities are consistent with motions that are dominated by the solar wind at distances ≳10 R ⊙, but the levels of frequency broadening for ≲10 R ⊙ require additional radial speeds ∼(100–300) km s−1 and/or transverse speeds ∼(20–70) km s−1. The inferred radial velocities also appear consistent with the sound or proton thermal speeds, while the speeds perpendicular to the radial direction are consistent with nonthermal motions measured via coronal Doppler-line broadening, interpreted as Alfvénic fluctuations. Landau damping of parallel propagating ion-sound (slow MHD) waves allows an estimate of the proton heating rate. The energy deposition rates due to ion-sound wave damping peak at a heliocentric distance of ∼(1–3) R ⊙ are comparable to the rates available from a turbulent cascade of Alfvénic waves at large scales, suggesting a coherent picture of energy transfer, via the cascade or/and parametric decay of Alfvén waves to the small scales where heating takes place.

On the Heating of the Slow Solar Wind by Imbalanced Alfvén-wave Turbulence from 0.06 to 1 au: Parker Solar Probe and Solar Orbiter Observations

In this work we analyze plasma and magnetic field data provided by the Parker Solar Probe and Solar Orbiter missions to investigate the radial evolution of the heating of Alfvénic slow wind by imbalanced Alfvén-wave (AW) turbulent fluctuations from 0.06 to 1 au. in our analysis we focus on slow solar-wind intervals with highly imbalanced and incompressible turbulence (i.e., magnetic compressibility C B = δ B/B ≤ 0.25, plasma compressibility C n = δ n/n ≤ 0.25, and normalized cross helicity σ c ≥ 0.65). First, we estimate the AW turbulent dissipation rate from the wave energy equation and find that the radial profile trend is similar to the proton heating rate. Second, we find that the scaling of the empirical AW turbulent dissipation rate Q W obtained from the wave energy equation matches the scaling from the phenomenological AW turbulent dissipation rate Q CH09 (with Q CH09 ≃ 1.55Q W ) derived by Chandran & Hollweg based on the model of reflection-driven turbulence. Our results suggest that, as in the fast solar wind, AW turbulence plays a major role in the ion heating that occurs in incompressible slow-wind streams.

Turbulence, and Proton and Electron Heating Rates in the Solar Corona: Analytical Approach

Analytical solutions for 2D and slab turbulence energies in the solar corona are presented, including a derivation of the corresponding correlation lengths, with implications for the proton and electron temperatures in the solar corona. These solutions are derived by solving the transport equations for 2D and slab turbulence energies and their correlation lengths, as well as proton and electron pressures. The solutions assume background profiles for the solar wind speed, solar wind mass density, and Alfvén velocity. Our analytical solutions can be related to those obtained from joint Parker Solar Probe and Solar Orbiter Metis coronagraph observations, as reported in Telloni et al. We find that the solution for 2D turbulence energy in the absence of nonlinear dissipation decreases more slowly compared to the dissipative solution. The solution for slab turbulence energy with no dissipation exhibits a more rapid increase compared to the dissipative solution. The proton heating rate is found to be about 82% of the total plasma heating rate at 6.3 R ⊙, which gradually decreases with increasing distance, eventually becoming ∼80% of the total plasma heating rate at ∼13 R ⊙, consistent with that found by Bandyopadhyay et al. (2023). These analytical solutions provide valuable insight for our understanding of turbulence, and its effect on proton and electron heating rates, in the solar corona. We compare the numerically solved turbulent transport equations for the 2D and slab turbulence energies, correlation lengths, and proton and electron pressures with the analytical solutions, finding good agreement between them.

Ion Heating by a Fast Magnetosonic Turbulence in the Solar Corona

Observational data at heliocentric distances of tens of solar radii suggest that fast magnetosonic modes make up a considerable fraction of the solar wind fluctuations. Furthermore, this fraction appears to increase closer to the Sun. We carry out three-dimensional kinetic simulations with particle ions and fluid electrons to evaluate the proton and alpha-particle heating produced by the damping of the fast waves in the solar corona. Realistic parameters at 5 solar radii, including the fluctuation amplitude, are used. We show that, due to the cyclotron resonance, the alphas are heated preferentially perpendicularly to the magnetic field and much more strongly than the protons. The presence of the alpha particles alters the energy partition by reducing the heating of the protons. Nevertheless, the proton heating is sufficient to account for the solar wind acceleration.

Eco-friendly multi-heat recovery applied to an innovative integration of flue gas-driven multigeneration process and geothermal power plant: Feasibility characterization from thermo-economic-environmental aspect

Sustainable production presents a viable approach that provides an environmentally friendly and integrated method for polygeneration objectives. This method can make the most significant impact in improving the effectiveness of conventional power plants. Furthermore, using renewable energy sources to modify the configuration of conventional power plants is imperative for implementing this methodology. Therefore, the primary objective of this research is to suggest a new method for attaining sustainable production in a power plant by integrating an environmentally friendly multi-heat recovery system. This innovative system allows for the efficient use of the power plant's flue gas for a polygeneration process and a geothermal power plant. The integrated setup comprises various components such as a multi-effect desalination unit, a proton exchange membrane electrolyzer, a cooling and heating generation subsystem, a liquefied natural gas regasification unit, a geothermal-based subsystem utilizing a flash-binary geothermal power plant, a Kalina cycle, and a heating generation unit. The study simulates this process using Aspen HYSYS software and conducts a comprehensive energy, exergy, economic, and environmental analysis. According to the results, the assessment reveals that the total energy and exergy efficiencies amount to 64.82% and 88.57%, respectively. The energy cost index is recorded at 0.028 $/kWh, alongside a specific CO2 emission of 0.211 kg/kWh. This value shows a notable reduction of 59.33% compared to a system reliant on biomass fuel. Parametric assessments are additionally conducted, whereby variations in performance metrics are predicted to exhibit the process performance.

Mind the gap: non-local cascades and preferential heating in high-β Alfvénic turbulence

ABSTRACT Characterizing the thermodynamics of turbulent plasmas is key to decoding observable signatures from astrophysical systems. In magnetohydrodynamic (MHD) turbulence, non-linear interactions between counter-propagating Alfvén waves cascade energy to smaller spatial scales where dissipation heats the protons and electrons. When the thermal pressure far exceeds the magnetic pressure, linear theory predicts a spectral gap at perpendicular scales near the proton gyroradius where Alfvén waves become non-propagating. For simple models of an MHD turbulent cascade that assume only local non-linear interactions, the cascade halts at this gap, preventing energy from reaching smaller scales where electron dissipation dominates, leading to an overestimate of the proton heating rate. In this work, we demonstrate that non-local contributions to the cascade, specifically large-scale shearing and small-scale diffusion, can bridge the non-propagating gap, allowing the cascade to continue to smaller scales. We provide an updated functional form for the proton-to-electron heating ratio accounting for this non-local energy transfer by evaluating a non-local weakened cascade model over a range of temperature and pressure ratios. In plasmas where the thermal pressure dominates the magnetic pressure, we observe that the proton heating is moderated compared to the significant enhancement predicted by local models.

Local Proton Heating at Magnetic Discontinuities in Alfvénic and Non-Alfvénic Solar Wind

We investigate the local proton energization at magnetic discontinuities/intermittent structures and the corresponding kinetic signatures in velocity phase space in Alfvénic (high cross helicity) and non-Alfvénic (low cross helicity) wind streams observed by Parker Solar Probe. By means of the partial variance of increments method, we find that the hottest proton populations are localized around compressible, coherent magnetic structures in both types of wind. Analysis of parallel and perpendicular temperature distributions suggest that the Alfvénic wind undergoes preferential enhancements of T ∥ at such structures, whereas the non-Alfvénic wind experiences preferential T ⊥ enhancements. Although proton beams are present in both types of wind, the proton velocity distribution function displays distinct features. Hot beams, i.e., beams with beam-to-core perpendicular temperature T ⊥,b /T ⊥,c up to three times larger than the total distribution anisotropy, are found in the non-Alfvénic wind, whereas colder beams are in the Alfvénic wind. Our data analysis is complemented by 2.5D hybrid simulations in different geometrical setups, which support the idea that proton beams in Alfvénic and non-Alfvénic wind have different kinetic properties and different origins. The development of a perpendicular nonlinear cascade, favored in balanced turbulence, allows a preferential relative enhancement of the perpendicular plasma temperature and the formation of hot beams. Cold field-aligned beams are instead favored by Alfvén wave steepening. Non-Maxwellian distribution functions are found near discontinuities and intermittent structures, pointing to the fact that the nonlinear formation of small-scale structures is intrinsically related to the development of highly nonthermal features in collisionless plasmas. Our results contribute to understanding the role of different coherent structures in proton energization and their implication in collisionless energy dissipation processes in space plasmas.

Lowering the reactor breakeven requirements for proton–boron 11 fusion

Recently, it has been shown that altering the natural collisional power flow of the proton–boron 11 (pB11) fusion reaction can significantly reduce the Lawson product of ion density and confinement time required to achieve ignition. However, these products are still onerous—on the order of 7×1015 cm−3 s under the most optimistic scenarios. Fortunately, a breakeven fusion power plant does not require an igniting plasma, but rather a reactor that produces more electrical power than it consumes. Here, we extend the existing 0D power balance analysis to check the conditions on power plant breakeven. We find that even for the base thermonuclear reaction, modern high-efficiency thermal engines should reduce the Lawson product to 1.2×1015 cm−3 s. We then explore the impact of several potential improvements, including fast proton heating, alpha power capture, direct conversion, and efficient heating. We find that such improvements could reduce the required Lawson product by a further order of magnitude, bringing aneutronic fusion to target ITER ion densities and confinement times.

On the Energy Coupling From Magnetosonic Waves to High‐Frequency Electromagnetic Ion Cyclotron Waves: Statistical Analysis

AbstractIn the inner magnetosphere, fast magnetosonic waves (MS waves) are known to resonantly interact with ring current protons, causing these protons to gain energy preferentially in the direction perpendicular to the background magnetic field. An anisotropic distribution of enhanced ring current protons is a necessary condition to excite electromagnetic ion cyclotron (EMIC) waves which are known to facilitate a rapid depletion of ultra‐relativistic electrons in the outer radiation belt. So, when a simultaneous observation of high‐frequency EMIC (HFEMIC) waves, anisotropic low‐energy protons, and MS waves was first reported, a chain of energy flow from MS waves to HFEMIC waves through proton heating was naturally proposed. In this study, we carry out a statistical analysis using Van Allen Probes data to provide deeper insights into this energy pathway. Our results show that the occurrence of HFEMIC waves exhibits good correlation with the enhanced flux and anisotropy of low‐energy protons, but the correlation between the low‐energy protons and the concurrent MS waves is rather poor. The latter result is given support by quasilinear diffusion analysis, indicating negligible momentum diffusion rates at sub‐keV energies, unless MS wave frequency gets very close to the proton cyclotron frequency (which constitutes only a small number of the cases). The fact that the first chain of the coupling is statistically inconclusive calls for an alternative explanation for the major source of the low‐energy anisotropic proton population in the inner magnetosphere.

Estimates of Proton and Electron Heating Rates Extended to the Near-Sun Environment

A central problem of space plasma physics is how protons and electrons are heated in a turbulent, magnetized plasma. The differential heating of charged species due to dissipation of turbulent fluctuations plays a key role in solar wind evolution. Measurements from previous heliophysics missions have provided estimates of proton and electron heating rates beyond 0.27 au. Using Parker Solar Probe (PSP) data accumulated during the first 10 encounters, we extend the evaluation of the individual rates of heat deposition for protons and electrons to a distance of 0.063 au (13.5 R ⊙) in the newly formed solar wind. The PSP data in the near-Sun environment show different behavior of the electron heat conduction flux from what was predicted from previous fits to Helios and Ulysses data. Consequently, the empirically derived proton and electron heating rates exhibit significantly different behavior than previous reports, with the proton heating becoming increasingly dominant over electron heating at decreasing heliocentric distances. We find that the protons receive about 80% of the total plasma heating at ≈13 R ⊙, slightly higher than the near-Earth values. This empirically derived heating partition between protons and electrons will help to constrain theoretical models of solar wind heating.

Statistical Study of Anisotropic Proton Heating in Interplanetary Magnetic Switchbacks Measured by Parker Solar Probe

Magnetic switchbacks, which are large angular deflections of the interplanetary magnetic field, are frequently observed by Parker Solar Probe (PSP) in the inner heliosphere. Magnetic switchbacks are believed to play an important role in the heating of the solar corona and the solar wind as well as the acceleration of the solar wind in the inner heliosphere. Here, we analyze magnetic field data and plasma data measured by PSP during its second and fourth encounters, and select 71 switchback events with reversals of the radial component of the magnetic field at times of unchanged electron-strahl pitch angles. We investigate the anisotropic thermal kinetic properties of plasma during switchbacks in a statistical study of the measured proton temperatures in the parallel and perpendicular directions as well as proton density and specific proton fluid entropy. We apply the “genetic algorithm” method to directly fit the measured velocity distribution functions in field-aligned coordinates using a two-component bi-Maxwellian distribution function. We find that the protons in most switchback events are hotter than the ambient plasma outside the switchbacks, with characteristics of parallel and perpendicular heating. Specifically, significant parallel and perpendicular temperature increases are seen for 45 and 62 of the 71 events, respectively. We find that the density of most switchback events decreases rather than increases, which indicates that proton heating inside the switchbacks is not caused by adiabatic compression, but is probably generated by nonadiabatic heating caused by field–particle interactions. Accordingly, the proton fluid entropy is greater inside the switchbacks than in the ambient solar wind.

Direct observation of solar wind proton heating from in situ plasma measurements

Aims. We determine the perpendicular and parallel proton heating rate in the solar wind, which is one of the primary goals of the Parker Solar Probe mission. Methods. To estimate the perpendicular and parallel proton heating rates from direct particle measurements by the SPAN electrostatic analyzers, the strong correlation between the proton temperature and the solar wind speed must be removed. This speed dependence is removed by normalization factors that convert the instantaneous temperature to the value it would have if the solar wind speed were 400 km s−1. One-hour and five-hour averages of the normalized perpendicular and parallel temperatures, measured on orbits 6–9, between 20 and 160 solar radii, are compared to the radial dependence they would have if there were no heating. Results. For the first time, perpendicular proton heating has been measured between 20 and 160 solar radii while there is neither heating nor cooling of the parallel protons below 70 solar radii. The extrapolated proton perpendicular temperature at one AU in a 400 km s−1 solar wind is 25 eV, which compares well with several earlier measurements. This result attests to the quality of the temperature measurements made by the particle detectors on the Parker Solar Probe. The heating rates, in ergs cm−3 s−1, that produced the observed perpendicular temperature are 6e−12 at 20 solar radii, 1e−13 at 50 solar radii, and 5e−14 at 160 solar radii.

On the Evaluation of Solar Wind's Heating Rates

AbstractSolar wind heating rates have often been calculated by fitting plasma and magnetic field data with a set of model functions. In this letter, we show that the rates obtained by such an approach strongly depend on the rather arbitrary choice one makes for these model functions. An alternative approach, consisting in monitoring the radial evolution of the adiabatic invariants, based on locally and consistently measured plasma and magnetic field parameters, is free from such a flaw. We apply this technique to a recently released Helios proton data set, and confirm the existence of a clear perpendicular heating of solar wind's protons. On the other hand, no significant change in the parallel adiabatic invariant is visible in the data. We conclude that to date, and in the distance range of 0.3–1 AU, no clear observation of a deviation of solar wind's protons from parallel adiabaticity has ever been made.

Quantifying the Agyrotropy of Proton and Electron Heating in Turbulent Plasmas

An important aspect of energy dissipation in weakly collisional plasmas is that of energy partitioning between different species (e.g., protons and electrons) and between different energy channels. Here we analyse pressure–strain interaction to quantify the fractions of isotropic compressive, gyrotropic, and nongyrotropic heating for each species. An analysis of kinetic turbulence simulations is compared and contrasted with corresponding observational results from Magnetospheric Multiscale Mission data in the magnetosheath. In assessing how protons and electrons respond to different ingredients of the pressure–strain interaction, we find that compressive heating is stronger than incompressive heating in the magnetosheath for both electrons and protons, while incompressive heating is stronger in kinetic plasma turbulence simulations. Concerning incompressive heating, the gyrotropic contribution for electrons is dominant over the nongyrotropic contribution, while for protons nongyrotropic heating is enhanced in both simulations and observations. Variations with plasma β are also discussed, and protons tend to gain more heating with increasing β.

Energy transfer of the solar wind turbulence based on Parker solar probe and other spacecraft observations

The supersonic solar wind, first predicted by Parker and then observed by Mariners, extends to form a heliosphere around the Sun. The energy supply from the energy containing range, the energy cascade though the inertial range, and the eventual energy dissipation are three basic processes of the energy transfer in the solar wind and have been studied for a long time. However, some basic issues remain to be discovered. Here, we review the recent progress in the mechanisms of energy transfer of the solar wind turbulence from the observational perspective. Based on the Parker solar probe observations, the energy supply mechanism by the low-frequency break sweeping is proposed to provide enough energy for the proton heating in the slow solar wind. This mechanism also works in the fast solar wind. The energy flux by the low-frequency break sweeping is consistent with that by the classical von Kármán decay mechanism. For the energy cascade in the inertial range, the scaling behavior of the third-order structure functions demonstrates the effect of the complex dynamics of the solar wind. The process of energy transfer is fundamental to understand the solar wind turbulence and help to construct the model of the space environment.

Proton and Helium Heating by Cascading Turbulence in a Low-beta Plasma

How ions are energized and heated is a fundamental problem in the study of energy dissipation in magnetized plasmas. In particular, the heating of heavy ions (including 4He2+, 3He2+, and others) has been a constant concern for understanding the microphysics of impulsive solar flares. In this article, via two-dimensional hybrid-kinetic particle-in-cell simulations, we study the heating of helium ions (4He2+) by turbulence driven by cascading waves launched at large scales from the left-handed polarized helium ion cyclotron wave branch of a multi-ion plasma composed of electrons, protons, and helium ions. We find significant parallel (to the background magnetic field) heating for both helium ions and protons due to the formation of beams and plateaus in their velocity distribution functions along the background magnetic field. The heating of helium ions in the direction perpendicular to the magnetic field starts with a lower rate than that in the parallel direction, but overtakes the parallel heating after a few hundreds of the proton gyro-periods due to cyclotron resonances with mainly obliquely propagating waves induced by the cascade of injected helium ion cyclotron waves at large scales. There is, however, little evidence for proton heating in the perpendicular direction due to the absence of left-handed polarized cyclotron waves near the proton cyclotron frequency. Our results are useful for understanding the preferential heating of 3He and other heavy ions in the 3He-rich solar energetic particle events, in which helium ions play a crucial role as a species of background ions regulating the kinetic plasma behavior.

Turbulent Energy Transfer and Proton–Electron Heating in Collisionless Plasmas

Despite decades of study of high-temperature weakly collisional plasmas, a complete understanding of how energy is transferred between particles and fields in turbulent plasmas remains elusive. Two major questions in this regard are how fluid-scale energy transfer rates, associated with turbulence, connect with kinetic-scale dissipation, and what controls the fraction of dissipation on different charged species. Although the rate of cascade has long been recognized as a limiting factor in the heating rate at kinetic scales, there has not been direct evidence correlating the heating rate with MHD-scale cascade rates. Using kinetic simulations and in situ spacecraft data, we show that the fluid-scale energy flux indeed accounts for the total energy dissipated at kinetic scales. A phenomenology, based on disruption of proton gyromotion by fluctuating electric fields that are produced in turbulence at proton scales, argues that the proton versus electron heating is controlled by the ratio of the nonlinear timescale to the proton cyclotron time and by the plasma beta. The proposed scalings are supported by the simulations and observations.

Relation between magnetosonic waves and pitch angle anisotropy of warm protons

In the past decade, many observations of transversely heated low energy protons were reported in the inner magnetosphere. Interestingly, most of the time heated protons were observed along with magnetosonic waves. Due to the strong correlation, it was often assumed that magnetosonic waves were responsible for the heating of low energy protons. By performing a case study under unusually disturbed geomagnetic conditions, this paper unravels the controversial relationship between the observed pitch angle anisotropy of warm protons and the accompanying magnetosonic waves in the inner magnetosphere. We perform a comparative analysis involving two nearly identical cases of pitch angle anisotropy of warm protons in low L-shell region–one with magnetosonic waves and one without them. It is found that magnetosonic waves are not responsible for primary heating of low-energy protons and may just marginally alter the shape of the distribution of heated protons in the events analyzed. Based on the recent Cluster and POLAR observations, we also show how the recirculated polar wind plasma in the Earth’s magnetosphere can cause the concurrent appearance of heated protons and magnetosonic waves.

Association of intermittency with electron heating in the near-Sun solar wind

ABSTRACT Several studies in the near-Earth environment show that intermittent structures are important sites of energy dissipation and particle energization. Recent Parker Solar Probe (PSP) data, sampled in the near-Sun environment, have shown that proton heating is concentrated near coherent structures, suggesting local heating of protons by turbulent cascade in this region. However, whether electrons exhibit similar behaviour in the near-Sun environment is not clear. Here, we address this question using PSP data collected near the Sun during the first seven orbits. We use the partial variance of increments (PVI) technique to identify coherent structures. We find that electron temperature is preferentially enhanced near strong discontinuities. Our results provide strong support for the inhomogeneous heating of electrons in the ‘young’ solar wind associated with the dissipation of turbulent fluctuations near intermittent structures.