Proton Heating Research Articles

Preferential Heating of Protons over Electrons from Coherent Structures during the First Perihelion of the Parker Solar Probe

The solar wind undergoes significant heating as it propagates away from the Sun; the exact mechanisms responsible for this heating remain unclear. Using data from the first perihelion of the Parker Solar Probe mission, we examine the properties of proton and electron heating occurring within magnetic coherent structures identified by means of the Partial Variance of Increments (PVI) method. Statistically, regions of space with strong gradients in the magnetic field, PVI ≥ 1, are associated with strongly enhanced proton but only slightly elevated electron temperatures. Our analysis indicates a heating mechanism in the nascent solar wind environment facilitated by a nonlinear turbulent cascade that preferentially heats protons over electrons.

Proton Heating by a Proton–Alpha Drift Instability with an Anisotropic Alpha-particle Temperature in a Turbulent Solar-wind Plasma

The proton–alpha drift instability is a possible mechanism of the alpha-particle deceleration and the resulting proton heating in the solar wind. We present hybrid numerical simulations of this instability with particle-in-cell ions and a quasi-neutralizing electron fluid for typical conditions at 1 au. For the parameters used in this paper, we find that fast magnetosonic unstable modes propagate only in the direction opposite to the alpha-particle drift and do not produce the perpendicular proton heating necessary to accelerate the solar wind. Alfvén modes propagate in both directions and heat the protons perpendicularly to the mean magnetic field. Despite being driven by the alpha temperature anisotropy, the Alfvén instability also extracts the energy from the bulk motion of the alpha particles. In the solar wind, the instabilities operate in a turbulent ambient medium. We show that the turbulence suppresses the Alfvén instability but the perpendicular proton heating persists. Unlike a static nonuniform background, the turbulence does not invert the sense of the proton heating associated with the fast magnetosonic instability and it remains preferentially parallel.

A Statistical Study of Pancake Pitch Angle Distribution of Low‐Energy Protons and Their Correlation With Magnetosonic Waves

AbstractWe performed a statistical study of the proton pancake pitch angle distributions (PADs) at the energy from 10 to 300 eV with the Helium Oxygen Proton Electron instrument on board the Van Allen Probes. The occurrence rate of low energy proton pancake PADs and their dependence on the energy, L shell, magnetic local time (MLT) and AL* index are analyzed. The results indicate that: (a) the occurrence rate of pancake PADs decreases as the proton energy increases; (b) under active geomagnetic activities (AL* < −300 nT), pancake PADs preferentially occur in the dayside; (c) under weak geomagnetic activities (AL* > −100 nT), the occurrence rate of pancake PADs has little dependence on MLT. We further discuss the contribution of magnetosonic (MS) waves on the formation of proton pancake PADs at low energy. The strong correlation between the occurrence of pancake PADs and the appearance of MS waves indicates that MS waves contribute to the formation of low energy proton pancake PADs. Moreover, the proton diffusion coefficients caused by MS waves suggest that MS waves can cause the proton heating at low energies in high density regions.

Statistical Analysis of Intermittency and its Association with Proton Heating in the Near-Sun Environment

Abstract We use data from the first six encounters of the Parker Solar Probe and employ the partial variance of increments (PVI) method to study the statistical properties of coherent structures in the inner heliosphere with the aim of exploring physical connections between magnetic field intermittency and observable consequences such as plasma heating and turbulence dissipation. Our results support proton heating localized in the vicinity of, and strongly correlated with, magnetic structures characterized by PVI ≥ 1. We show that, on average, such events constitute ≈19% of the data set, though variations may occur depending on the plasma parameters. We show that the waiting time distribution (WT) of identified events is consistent across all six encounters following a power-law scaling at lower WTs. This result indicates that coherent structures are not evenly distributed in the solar wind but rather tend to be tightly correlated and form clusters. We observe that the strongest magnetic discontinuities, PVI ≥ 6, usually associated with reconnection exhausts, are sites where magnetic energy is locally dissipated in proton heating and are associated with the most abrupt changes in proton temperature. However, due to the scarcity of such events, their relative contribution to energy dissipation is minor. Taking clustering effects into consideration, we show that smaller scale, more frequent structures with PVI between 1 ≲ PVI ≲ 6 play a major role in magnetic energy dissipation. The number density of such events is strongly associated with the global solar wind temperature, with denser intervals being associated with higher T p .

The Yaglom Scaling of the Third-order Structure Functions in the Inner Heliosphere Observed by Helios 1 and 2

Abstract The third-order scaling law, Yaglom law, of Elsässer fluctuations in the solar wind is believed to reflect the inertial range energy cascade of the MHD turbulence and provides an approach to evaluate the cascade rate. However, the occurrence ratio with the Yaglom scaling law, the fraction of the intervals where the Yaglom linear scaling is observed, is reported to be low (0.05–0.30) in the high-latitude solar wind observed by the Ulysses spacecraft. Whether the occurrence ratio could be higher in other conditions remains unknown. Here, we analyze the occurrence of the third-order scaling in the inner heliosphere with the first 100 days of observation of the Helios 1 and Helios 2 spacecraft. We investigate 162 intervals in the leading edges and 323 intervals in the trailing edges of the high-speed streams, respectively. All of these intervals have a time duration of 9 hr. We find that in the inner heliosphere the occurrence ratio is relatively high in the leading edges (0.58) and moderate in the trailing edges (0.45). Among the data intervals with the Yaglom scaling in the leading edges, 94.7% of intervals give positive rates, while in the trailing edges 78.6% give negative rates. The variations of the occurrence ratio with various turbulence parameters are shown. The cascade rate is found to be higher than the proton heating rate calculated from the data, which have third-order scaling. These new results raise several questions related to the nature and origin of the third-order scaling law and may initiate new studies on solar wind turbulence.

Improving the Alfvén Wave Solar Atmosphere Model Based on Parker Solar Probe Data

Abstract In van der Holst et al. (2019), we modeled the solar corona and inner heliosphere of the first encounter of NASA’s Parker Solar Probe (PSP) using the Alfvén Wave Solar atmosphere Model (AWSoM) with Air Force Data Assimilative Photospheric flux Transport–Global Oscillation Network Group magnetograms, and made predictions of the state of the solar wind plasma for the first encounter. AWSoM uses low-frequency Alfvén wave turbulence to address the coronal heating and acceleration. Here, we revise our simulations, by introducing improvements in the energy partitioning of the wave dissipation to the electron and anisotropic proton heating and using a better grid design. We compare the new AWSoM results with the PSP data and find improved agreement with the magnetic field, turbulence level, and parallel proton plasma beta. To deduce the sources of the solar wind observed by PSP, we use the AWSoM model to determine the field line connectivity between PSP locations near the perihelion at 2018 November 6 UT 03:27 and the solar surface. Close to the perihelion, the field lines trace back to a negative-polarity region about the equator.

Unusual high frequency EMIC waves: Detailed analysis of EMIC wave excitation and energy coupling between EMIC and magnetosonic waves

• Testing high frequency EMIC waves generation by anisotropic suprathermal protons. • Cyclotron resonance with magnetosonic waves is inefficient in thermal proton heating. • Quantitative understanding of the magnetosonic-EMIC energy coupling process is needed. A recent event study suggested a coupling process whereby suprathermal protons (10–100 eV), as a result of perpendicular heating by pre-existing magnetosonic waves, can excite electromagnetic ion cyclotron (EMIC) waves with frequency near the local proton cyclotron frequency ( f ~ 0.95 f cp ). The present study tests this coupling process. First, one-dimensional hybrid (kinetic ions/massless fluid electrons) simulations of parallel-propagating EMIC waves initialized with the plasma conditions derived from the event prove that high frequency EMIC waves can be generated by anisotropic suprathermal protons instead of more energetic (10s of keV) ring current protons. Calculation of the quasilinear pitch-angle diffusion coefficient for electrons using the simulated waves suggests that these high frequency EMIC waves outside the plasmasphere can play a role in the pitch-angle scattering of ~ MeV electrons due to the large wavenumber of the excited EMIC waves. Second, the role of the pre-existing magnetosonic waves in the suprathermal proton heating is examined using quasilinear diffusion theory and simple test particle calculation. It is found that the quasilinear diffusion becomes ineffective in energies relevant to the suprathermal protons, indicating that the low-energy ( < 10 eV) protons cannot be efficiently energized to the observed level through multi-harmonic cyclotron resonances with the magnetosonic waves observed. Rather, some kind of non-resonant process may have been at play, if the magnetosonic waves were actually involved in the heating. This result suggests that more quantitative understanding of the suggested energy coupling process through magnetosonic waves is needed.

Large-scale Structure and Turbulence Transport in the Inner Solar Wind: Comparison of Parker Solar Probe’s First Five Orbits with a Global 3D Reynolds-averaged MHD Model

Abstract Simulation results from a global magnetohydrodynamic model of the solar corona and solar wind are compared with Parker Solar Probe (PSP) observations during its first five orbits. The fully three-dimensional model is based on Reynolds-averaged mean-flow equations coupled with turbulence-transport equations. The model includes the effects of electron heat conduction, Coulomb collisions, turbulent Reynolds stresses, and heating of protons and electrons via a turbulent cascade. Turbulence-transport equations for average turbulence energy, cross helicity, and correlation length are solved concurrently with the mean-flow equations. Boundary conditions at the coronal base are specified using solar synoptic magnetograms. Plasma, magnetic field, and turbulence parameters are calculated along the PSP trajectory. Data from the first five orbits are aggregated to obtain trends as a function of heliocentric distance. Comparison of simulation results with PSP data shows good agreement, especially for mean-flow parameters. Synthetic distributions of magnetic fluctuations are generated, constrained by the local rms turbulence amplitude given by the model. Properties of this computed turbulence are compared with PSP observations.

The Transport and Evolution of MHD Turbulence throughout the Heliosphere: Models and Observations

A detailed study of solar wind turbulence throughout the heliosphere in both the upwind and downwind directions is presented. We use an incompressible magnetohydrodynamic (MHD) turbulence model that includes the effects of electrons, the separation of turbulence energy into proton and electron heating, the electron heat flux, and Coulomb collisions between protons and electrons. We derive expressions for the turbulence cascade rate corresponding to the energy in forward and backward propagating modes, the fluctuating kinetic and magnetic energy, the normalized cross-helicity, and the normalized residual energy, and calculate the turbulence cascade rate from 0.17 to 75 au in the upwind and downwind directions. Finally, we use the turbulence transport models to derive cosmic ray (CR) parallel and perpendicular mean free paths (mfps) in the upwind and downwind heliocentric directions. We find that turbulence in the upwind and downwind directions is different, in part because of the asymmetric distribution of new born pickup ions in the two directions, which results in the CR mfps being different in the two directions. This is important for models that describe the modulation of cosmic rays by the solar wind.

A simulation study of protons heated by left/right-handed Alfvén waves generated by electromagnetic proton–proton instability

Most protons in the solar wind belong to one of two different populations, the less dense beam protons and the denser core protons. The beam protons, with a velocity of (1–2) V A ( is the local Alfvén speed), always drift relative to the core protons; this kind of distribution is unstable and stimulates several kinds of wave mode. In this study, using a 2D hybrid simulation model, we find that the original right-handed elliptically polarized Alfvén waves become linearly polarized, and eventually become right-handed and circularly polarized. Given that linearly polarized waves are a superposition of left-handed and right-handed waves, cyclotron resonance in the right-handed/left-handed component heats beam/core protons perpendicularly. The resonance between beam protons and right-handed polarized waves is stronger when the beam relative density is lower, resulting in more dramatic perpendicular heating of beam protons, whereas the situation is reversed when the beam relative density is larger.

MAVEN Observations of Low Frequency Steepened Magnetosonic Waves and Associated Heating of the Martian Nightside Ionosphere

AbstractWe present Mars Atmosphere and Volatile EvolutioN (MAVEN) observations of low frequency steepened fast magnetosonic waves in the Martian magnetosphere and ionosphere. Solar wind pressure pulses generated in the upstream foreshock region impact the magnetopause and generate the magnetosonic waves within the magnetosphere, in a process analogous to the production of magnetic Pc pulsations in the terrestrial magnetosphere. The draped nature of the IMF about Mars, combined with the near‐perpendicular propagation of these waves across the magnetic field, act to channel these waves into the nightside ionosphere, where they are observed in their non‐linear steepened form. Coincident‐in‐time ion observations show that the light (H+) and heavy (O+, O2+, CO2+) planetary ion distribution functions possess significant suprathermal energetic tails, arising from wave‐particle interactions with the steepened waves. The short gyro period and small gyro radius of the protons, relative to the steepened waves, results in proton heating via adiabatic compression. In contrast, the long gyro period of the heavy ions relative to the wave frequency leads to nonadiabatic heating via wave‐trapping processes. The light and heavy ion species are heated above escape energy by these waves, even down close to the exobase. A limited statistical study of 101 neighboring orbits found that similar wave events occurred on 28% of orbits analyzed, suggesting that such wave‐heating events may be important drivers of the Mars nightside ionospheric dynamics and energy budget. Our discussion includes placing our results in the context of solar wind energy transfer to the ionospheres of unmagnetized and magnetized bodies in general.

Boundary Conditions at the Heliospheric Termination Shock with Pickup Ions

Abstract In a collisionless shock the directed flow energy is converted mainly in thermal energy of the plasma species. At the termination shock (TS) a substantial portion of energy goes into heating of pickup ions (PUIs), while heating of the solar wind protons (SW) is weaker than it would be without PUI. Heating of both species is nonadiabatic. Downstream pressure of the mixture is determined by conservation laws for the whole mixture. SW heating is sensitive to the details of the shock front, while heating of PUI is not. The profile is an analytical approximation of the observed TS. Here the downstream temperature and pressure of PUIs are obtained for the first time using test particle analysis in a model shock profile for various magnetic compression ratios and shock angles. The profile is an analytical approximation of the observed TS. The results of the analysis are used in the pressure balance equation and the corresponding SW heating is estimated. The analysis is supported by full particle simulations, except for the SW heating that was not studied using test particle data due to its apparent dependence on fine structure of the shock front.

Modeling proton and electron heating in the fast solar wind

Context. The Parker Solar Probe (PSP) measures solar wind protons and electrons near the Sun. To study the thermodynamic properties of electrons and protons, we include electron effects, such as distributed turbulent heating between protons and electrons, Coulomb collisions between protons and electrons, and heat conduction of electrons. Aims. We develop a general theoretical model of nearly incompressible magnetohydrodynamic (NI MHD) turbulence coupled with a solar wind model that includes electron pressure and heat flux. Methods. It is important to note that 60% of the turbulence energy is assigned to proton heating and 40% to electron heating. We use an empirical expression for the electron heat flux. We derived a nonlinear dissipation term for the residual energy that includes both the Alfvén effect and the turbulent small-scale dynamo effect. Similarly, we obtained the NI/slab time-scale in an NI MHD phenomenology to use in the derivation of the nonlinear term that incorporates the Alfvén effect. Results. A detailed comparison between the theoretical model solutions and the fast solar wind measured by PSP and Helios 2 shows that they are consistent. The results show that the nearly incompressible NI/slab turbulence component describes observations of the fast solar wind periods when the solar wind flow is aligned or antialigned with the magnetic field.

Turbulent Proton Heating Rate in the Solar Wind from 5–45 R ⊙

Abstract Various remote sensing observations have been used so far to probe the turbulent properties of the solar wind. Using the recently reported density modulation indices that are derived using angular broadening observations of Crab Nebula during 1952–2013, we measured the solar wind proton heating using the kinetic Alfvén wave dispersion equation. The estimated heating rates vary from ≈1.58 × 10−14 to 1.01 × 10−8 erg cm−3 s−1 in the heliocentric distance range of 5–45 R ⊙. Further, we found that heating rates vary with the solar cycle in correlation with density modulation indices. The models derived using in situ measurements (for example, electron/proton density, temperature, and magnetic field) that the recently launched Parker Solar Probe observations (planned closest perihelia 9.86 R ⊙ from the center of the Sun) are useful in the estimation of the turbulent heating rate precisely. Further, we compared our heating rate estimates with the one derived using previously reported remote sensing and in situ observations.

The Characteristics of EMIC Waves in the Magnetosphere Based on the Van Allen Probes and Arase Observations

AbstractWe performed a comprehensive statistical study of electromagnetic ion cyclotron (EMIC) waves observed by the Van Allen Probes and Exploration of energization and Radiation in Geospace satellite (ERG/Arase). From 2017 to 2018, we identified and categorized EMIC wave events with respect to wavebands (H+ and He+ EMIC waves) and relative locations from the plasmasphere (inside and outside the plasmasphere). We found that H+ EMIC waves in the morning sector at L &gt; 8 are predominantly observed with a mixture of linear and right‐handed polarity and higher wave normal angles during quiet geomagnetic conditions. Both H+ and He+ EMIC waves observed in the noon sector at L ∼ 4–6 have left‐handed polarity and lower wave normal angles at |MLAT| &lt; 20° during the recovery phase of a storm with moderate solar wind pressure. In the afternoon sector (12–18 MLT), He+ EMIC waves are dominantly observed with strongly enhanced wave power at L ∼ 6–8 during the storm main phase, while in the dusk sector (17–21 MLT) they have lower wave normal angles with linear polarity at L &gt; 8 during geomagnetic quiet conditions. Based on distinct characteristics at different EMIC wave occurrence regions, we suggest that EMIC waves in the magnetosphere can be generated by different free energy sources. Possible sources include the freshly injected particles from the plasma sheet, adiabatic heating by dayside magnetospheric compressions, suprathermal proton heating by magnetosonic waves, and off‐equatorial sources.

Magnetic Helicity Signature and Its Role in Regulating Magnetic Energy Spectra and Proton Temperatures in the Solar Wind

Abstract In a previous paper, we found that perpendicular and parallel proton temperatures are clearly associated with the proton-scale turbulence in the solar wind, and magnetic helicity signature appears to be an important indicator in the association. Based on 15 yr of in situ measurements, the present paper further investigates the magnetic helicity of solar wind turbulence and its role in regulating magnetic energy spectra and proton temperatures. Results show that the presence of the helicity signature is very common in solar wind turbulence at scales , with k being the wavenumber and ρ p the proton gyroradius. The sign of the helicity is mostly positive, indicating the dominance of right-handed polarization of the turbulence. The helicity magnitude usually increases with k and (the proton parallel beta) when and are less than unity. As helicity magnitude increases, the power index of the energy spectrum becomes more negative, and the proton temperatures and rise significantly, where and are the perpendicular and parallel temperatures with respect to the background magnetic field. In particular, the rise of is faster than when is satisfied. The faster rise of with the helicity magnitude may be interpreted as the result of the preferentially perpendicular heating of solar wind protons by kinetic Alfvén wave turbulence.

The Role of Parametric Instabilities in Turbulence Generation and Proton Heating: Hybrid Simulations of Parallel-propagating Alfvén Waves

Abstract Large-amplitude Alfvén waves tend to be unstable to parametric instabilities that result in a decay process of the initial wave into different daughter waves depending upon the amplitude of the fluctuations and the plasma beta. The propagation angle with respect to the mean magnetic field of the daughter waves plays an important role in determining the type of decay. In this paper, we revisit this problem by means of multidimensional hybrid simulations. In particular, we study the decay and the subsequent nonlinear evolution of large-amplitude Alfvén waves by investigating the saturation mechanism of the instability and its final nonlinear state reached for different wave amplitudes and plasma beta conditions. As opposed to one-dimensional simulations where the Decay instability is suppressed for increasing plasma beta values, we find that the decay process in multidimensions persists at large values of the plasma beta via the filamentation/magnetosonic decay instabilities. In general, the decay process acts as a trigger both to develop a perpendicular turbulent cascade and to enhance mean field-aligned wave–particle interactions. We find indeed that the saturated state is characterized by a turbulent plasma displaying a field-aligned beam at the Alfvén speed and increased temperatures that we ascribe to the Landau resonance and pitch-angle scattering in phase space.

Observational Evidence for Solar Wind Proton Heating by Ion‐Scale Turbulence

AbstractBased on in situ measurements by Wind spacecraft from 2005 to 2015, this letter reports for the first time a clearly scale‐dependent connection between proton temperatures and the turbulence in the solar wind. A statistical analysis of proton‐scale turbulence shows that increasing helicity magnitudes correspond to steeper magnetic energy spectra. In particular, there exists a positive power law correlation (with a slope ∼0.4) between the proton perpendicular temperature and the turbulent magnetic energy at scales , with k being the wave number and ρp being the proton gyroradius. These findings present evidence of solar wind heating by the proton‐scale turbulence. They also provide insight and observational constraint on the physics of turbulent dissipation in the solar wind.

Solar Wind Turbulence from 1 to 45 au. IV. Turbulent Transport and Heating of the Solar Wind Using Voyager Observations

Abstract We adopt the theory for turbulent transport of energy by solar wind fluctuations and apply that theory to observations by the Voyager 1 and 2 spacecraft to obtain rates of thermal proton heating that are controlled by two sources: the large-scale fluctuations in the solar wind that arise from solar sources and the excitation of waves by newborn interstellar ions. In the process, we compute magnetic spectra for 839 data intervals spanning the range from 1 to 35 au when thermal ion data is available and use those spectra to obtain independent estimates for the energy cascade rates at intermediate scales that we assume equals the rate of thermal proton heating by the turbulence. We compare three analyses that describe different aspects of the solar wind heating problem: the rate of energy cascade through the intermediate scales of the magnetic spectrum, the rate at which energy is supplied to that cascade from the large-scale fluctuations as described by magnetohydrodynamic transport theory, and the rate at which energy is injected into the spectrum via wave excitation by newborn interstellar ions. The first two expressions are found to be in good agreement while the latter source dynamics become important beyond 10 au.

Solar Wind Reconnection Exhausts in the Inner Heliosphere Observed by Helios and Detected via Machine Learning

Abstract Reconnecting current sheets in the solar wind play an important role in the dynamics of the heliosphere and offer an opportunity to study magnetic reconnection exhausts under a wide variety of inflow and magnetic shear conditions. However, progress in understanding reconnection can be frustrated by the difficulty of finding events in long time-series data. Here we describe a new method to detect magnetic reconnection events in the solar wind based on machine learning, and apply it to Helios data in the inner heliosphere. The method searches for known solar wind reconnection exhaust features, and parameters in the algorithm are optimized to maximize the Matthews Correlation Coefficient using a training set of events and non-events. Applied to the whole Helios data set, the trained algorithm generated a candidate set of events that were subsequently verified by hand, resulting in a database of 88 events. This approach offers a significant reduction in construction time for event databases compared to purely manual approaches. The database contains events covering a range of heliospheric distances from ∼0.3 to ∼1 au, and a wide variety of magnetic shear angles, but is limited by the relatively coarse time resolution of the Helios data. Analysis of these events suggests that proton heating by reconnection in the inner heliosphere depends on the available magnetic energy in a manner consistent with observations in other regimes such as at the Earth’s magnetopause, suggesting this may be a universal feature of reconnection.