Alfven Wave Heating Research Articles

A STUDY OF ALFVÉN WAVE PROPAGATION AND HEATING THE CHROMOSPHERE

Alfven wave propagation, reflection, and heating of the chromosphere are studied for a one-dimensional solar atmosphere by self-consistently solving plasma, neutral fluid, and Maxwell's equations with incorporation of the Hall effect and strong electron-neutral, electron-ion, and ion-neutral collisions. We have developed a numerical model based on an implicit backward difference formula of second-order accuracy both in time and space to solve stiff governing equations resulting from strong inter-species collisions. A non-reflecting boundary condition is applied to the top boundary so that the wave reflection within the simulation domain can be unambiguously determined. It is shown that due to the density gradient the Alfven waves are partially reflected throughout the chromosphere and more strongly at higher altitudes with the strongest reflection at the transition region. The waves are damped in the lower chromosphere dominantly through Joule dissipation, producing heating strong enough to balance the radiative loss for the quiet chromosphere without invoking anomalous processes or turbulences. The heating rates are larger for weaker background magnetic fields below ~500 km with higher-frequency waves subject to heavier damping. There is an upper cutoff frequency, depending on the background magnetic field, above which the waves are completely damped. At the frequencies below which the waves are not strongly damped, the interaction of reflected waves with the upward propagating waves produces power at their double frequencies, which leads to more damping. The wave energy flux transmitted to the corona is one order of magnitude smaller than that of the driving source.

Parameterisation of coronal heating: spatial distribution and observable consequences

We investigate the difference in the spatial distribution of the energy input for parametrizations of different mechanisms to heat the corona of the Sun and possible impacts on the coronal emission. We use a 3D MHD model of a solar active region as a reference and compare the Ohmic-type heating in this model to parametrizations for alternating current (AC) and direct current (DC) heating models, in particular, we use Alfven wave and MHD turbulence heating. We extract the quantities needed for these two parametrizations from the reference model and investigate the spatial distribution of the heat input in all three cases, globally and along individual field lines. To study differences in the resulting coronal emission we employ 1D loop models with a prescribed heat input based on the heating rate we extracted along a bundle of field lines. On average, all heating implementations show a roughly drop of the heating rate with height. This also holds for individual field lines. While all mechanism show a concentration of the energy input towards the low parts of the atmosphere, for individual field lines the concentration towards the footpoints is much stronger for the DC mechanisms than for the Alfven wave AC case. In contrast, the AC model gives a stronger concentration of the emission towards the footpoints. This is because the more homogeneous distribution of the energy input leads to higher coronal temperatures and a more extended transition region. The significant difference in the concentration of the heat input towards the foot points for the AC and DC mechanisms, and the pointed difference in the spatial distribution of the coronal emission for these cases shows that the two mechanisms should be discriminable by observations. Before drawing final conclusions, these parametrizations should be implemented in new 3D models in a more self-consistent way.

The Ion Cyclotron, Lower Hybrid and Alfven Wave Heating Methods

This lecture covers the practical features and experimental results of the three heating methods. The emphasis is on ion cyclotron heating. First, we briefly come back to the main non-collisional heating mechanisms and to the particular features of the quasilinear coefficient in the ion cyclotron range of frequencies (ICRF). The specific case of the ion-ion hybrid resonance is treated, as well as the polarisation issue and minority heating scheme. The various ICRF scenarios are reviewed. The experimental applications of ion cyclotron resonance heating (ICRH) systems are outlined. Then, the lower hybrid and Alfvén wave heating and current drive experimental results are covered more briefly. Where applicable, the prospects for ITER are commented.

THE ROLE OF TORSIONAL ALFVÉN WAVES IN CORONAL HEATING

In the context of coronal heating, among the zoo of MHD waves that exist in the solar atmosphere, Alfven waves receive special attention. Indeed, these waves constitute an attractive heating agent due to their ability to carry over the many different layers of the solar atmosphere sufficient energy to heat and maintain a corona. However, due to their incompressible nature these waves need a mechanism such as mode conversion (leading to shock heating), phase mixing, resonant absorption or turbulent cascade in order to heat the plasma. New observations with polarimetric, spectroscopic and imaging instruments such as those on board of the japanese satellite Hinode, or the SST or CoMP, are bringing strong evidence for the existence of energetic Alfven waves in the solar corona. In order to assess the role of Alfven waves in coronal heating, in this work we model a magnetic flux tube being subject to Alfven wave heating through the mode conversion mechanism. Using a 1.5-dimensional MHD code we carry out a parameter survey varying the magnetic flux tube geometry (length and expansion), the photospheric magnetic field, the photospheric velocity amplitudes and the nature of the waves (monochromatic or white noise spectrum). It is found that independently of the photospheric wave amplitude and magnetic field a corona can be produced and maintained only for long (> 80 Mm) and thick (area ratio between photosphere and corona > 500) loops. Above a critical value of the photospheric velocity amplitude (generally a few km/s) the corona can no longer be maintained over extended periods of time and collapses due to the large momentum of the waves. These results establish several constraints on Alfven wave heating as a coronal heating mechanism, especially for active region loops.

The Ion Cyclotron, Lower Hybrid and Alfven Wave Heating Methods

This lecture covers the practical features and experimental results of the three heating methods. The emphasis is on ion cyclotron heating. First, we briefly come back to the main non-collisional heating mechanisms and to the particular features of the quasilinear coefficient in the ion cyclotron range of frequencies (ICRF). The specific case of the ion-ion hybrid resonance is treated, as well as the polarisation issue and minority heating scheme. The various ICRF scenarios are reviewed. The experimental applications of ion cyclotron resonance heating (ICRH) systems are outlined. Then, the lower hybrid and Alfvén wave heating and current drive experimental results are covered more briefly. Where applicable, the prospects for ITER are commented.

The Ion Cyclotron, Lower Hybrid and Alfven Wave Heating Methods

This lecture covers the practical features and experimental results of the three heating methods. The emphasis is on ion cyclotron heating. First, we briefly come back to the main non-collisional heating mechanisms and to the particular features of the quasilinear coefficient in the ion cyclotron range of frequencies (ICRF). The specific case of the ion-ion hybrid resonance is treated, as well as the polarisation issue and minority heating scheme. The various ICRF scenarios are reviewed. The experimental applications of ion cyclotron resonance heating (ICRH) systems are outlined. Then, the lower hybrid and Alfvén wave heating and current drive experimental results are covered more briefly. Where applicable, the prospects for ITER are commented.

Sunspot Chromospheric Heating by Kinetic Alfvén Waves

Sunspot atmospheric models show that sunspots have a higher temperature than the surrounding quiet Sun in the upper chromosphere, although they are dark in the photosphere. This Letter presents a comparison between acoustic wave heating and kinetic Alfven wave (KAW) heating in sunspots from the photosphere through the chromosphere based on a semiempirical model calculated by non-LTE procedure. The result suggests that acoustic wave heating is still a possible dominating mechanism in the photosphere and in the lower chromosphere below 850 km, similar to previous works. But in the upper chromosphere above 850 km, KAW heating is a more promising candidate that dominates sunspot chromospheric heating. We speculate that this probably relates to the ionization exceeding one in a thousand in the upper chromosphere, so that the plasma processes such as KAW dissipation play an important role in the atmospheric dynamics.

Fast Alfven Wave Heating and Acceleration of Ions in a Nonuniform Magnetoplasma

A test-particle approach is used to study the collisionless response of protons to cold plasma fast Alfven waves propagating in a nonuniform magnetic field: specifically, a two-dimensional X-point field. The field perturbations associated with the waves, which are assumed to be azimuthally symmetric and invariant in the direction orthogonal to the X-point plane, are exact solutions of the linearized ideal magnetohydrodynamic (MHD) equations. The protons are initially Maxwellian, at temperatures that are consistent with the cold plasma approximation. Two kinds of wave solution are invoked: global perturbations, with inward- and outward-propagating components; and localized purely inward-propagating waves, the wave electric field E having a preferred direction. In both cases the protons are effectively heated in the direction parallel to the magnetic field, although the parallel velocity distribution is generally non-Maxwellian and some protons are accelerated to highly suprathermal energies. This heating and acceleration can be attributed to the fact that protons undergoing E × B drifts due to the presence of the wave are subject to a force in the direction parallel to B. The localized wave solution produces more effective proton heating than the global solution, and successive wave pulses have a synergistic effect. This process, which could play a role in both solar coronal heating and late-phase heating in solar flares, is effective for all ion species, but it has a negligible direct effect on electrons. However, both electrons and heavy ions would be expected to acquire a temperature comparable to that of the protons on collisional timescales.

The reversed effect of the electromagnetic wave spatial multimodality on Alfven wave heating in a helical magnetic field

Spatial distribution of electromagnetic wave fields within the local Alfven resonance (AR) region is studied under the conditions when this distribution is governed just by a helical inhomogeneity of the confining magnetic field rather than electron inertia or finite ion Larmor radius. It is shown that accounting for the helical inhomogeneity of the steady magnetic field can remove the infinite discontinuity of the wave fields that takes place in the case of straight magnetic field rather than other weak effects. Radio frequency (RF) power absorption within the local AR region is compared with the case when AR structure is governed by other weak phenomena.

The Ion Cyclotron, Lower Hybrid and Alfven Wave Heating Methods

This lecture covers the practical features and experimental results of the three heating methods. The emphasis is on ion cyclotron heating. First, we briefly come back to the main non-collisional heating mechanisms and to the particular features of the quasilinear coefficient in the ion cyclotron range of frequencies (ICRF). The specific case of the ion-ion hybrid resonance is treated, as well as the polarisation issue and minority heating scheme. The various ICRF scenarios are reviewed. The experimental applications of ion cyclotron resonance heating (ICRH) systems are outlined. Then, the lower hybrid and Alfvén wave heating and current drive experimental results are covered more briefly. Where applicable, the prospects for ITER are commented.

The Ion Cyclotron, Lower Hybrid, and Alfven Wave Heating Methods

This lecture covers the practical features and experimental results of the three heating methods. The emphasis is on ion cyclotron heating. First, we briefly come back to the main non-collisional heating mechanisms and to the particular features of the quasilinear coefficient in the ion cyclotron range of frequencies (ICRF). The specific case of the ion-ion hybrid resonance is treated, as well as the polarisation issue and minority heating scheme. The various ICRF scenarios are reviewed. The experimental applications of ion cyclotron resonance heating (ICRH) systems are outlined. Then, the lower hybrid and Alfvén wave heating and current drive experimental results are covered more briefly. Where applicable, the prospects for ITER are commented.

Global Alfven Wave Heating of the Magnetosphere of Young Stars

Excitation of a global Alfvén wave (GAW) is proposed as a viable mechanism to explain plasma heating in the magnetosphere of young stars. The wave and basic plasma parameters are compatible with the requirement that the dissipation length of GAWs be comparable to the distance between the shocked region at the star's surface and the truncation region in the accretion disk. A two-fluid magnetohydrodynamic plasma model is used in the analysis. A current-carrying filament along magnetic field lines acts as a waveguide for the GAWs. The current in the filament is driven by plasma waves along the magnetic field lines and/or by plasma crossing magnetic field lines in the truncated region of the disk of the accreting plasma. The conversion of a small fraction of the kinetic energy into GAW energy is sufficient to heat the plasma filament to observed temperatures.

The Ion Cyclotron, Lower Hybrid and Alfven Wave Heating Methods

This lecture covers the practical features and experimental results of the three heating methods. The emphasis is on ion cyclotron heating. First, we briefly come back to the main non-collisional heating mechanisms and to the particular features of the quasi linear coefficient in the ion cyclotron range of frequencies (ICRF). The specific case of the ion-ion hybrid resonance is treated, as well as the polarisation issue and minority heating scheme. The various ICRF scenarios are reviewed. The experimental applications of ion cyclotron resonance heating (ICRH) systems are outlined. Then, the lower hybrid and Alfvén wave heating and current drive experimental results are covered more briefly. Where applicable, the prospects for ITER are commented.

Interpretation of coronal off-limb spectral line width measurements

Spectral line widths measured above the solar limb have been used to infer wave velocity amplitude height dependencies, supporting Alfven wave coronal heating and wave driven solar wind models. Comparison of the inferred amplitude/density dependence with a constant magnetic field strength, undamped wave propagation model have shown good agreement, providing the first strong support of Alfven wave heating models. We derive the density dependence for wave propagation in an expanding flux tube with decreasing field strength, and show that the resulting density dependence is identical to that of the constant field strength case. We use the expanding flux tube propagation model to infer the wave amplitude in the low photosphere, which is a factor of 9 lower than granulation velocities.

The Ion Cyclotron, Lower Hybrid and Alfven Wave Heating Methods

This lecture covers the practical features and experimental results of the three heating methods. The emphasis is on ion cyclotron heating. First, we briefly come back to the main non-collisional heating mechanisms and to the particular features of the quasilinear coefficient in the ion cyclotron range of frequencies (ICRF). The specific case of the ion-ion hybrid resonance is treated, as well as the polarisation issue and minority heating scheme. The various ICRF scenarios are reviewed. The experimental applications of ion cyclotron resonance heating (ICRH) systems are outlined. Then, the lower hybrid and Alfvén wave heating and current drive experimental results are covered more briefly. Where applicable, the prospects for ITER are commented.

A Simple Model of Nonlinear Diffusive Shock Acceleration

We present a simple model of nonlinear diffusive shock acceleration (also called first-order Fermi shock acceleration) that determines the shock modification, spectrum, and efficiency of the process in the plane-wave, steady state approximation as a function of an arbitrary injection parameter, η. The model, which uses a three-power-law form for the accelerated particle spectrum and contains only simple algebraic equations, includes the essential elements of the full nonlinear model and has been tested against Monte Carlo and numerical kinetic shock models. We include both adiabatic and Alfven wave heating of the upstream precursor. The simplicity and ease of calculation make this model useful for studying the basic properties of nonlinear shock acceleration, as well as providing results accurate enough for many astrophysical applications. It is shown that the shock properties depend upon the shock speed u0 with respect to a critical value u ηp, which is a function of the injection rate η and maximum accelerated particle momentum pmax. For u0 MA0, or by rtot ≈ 1.5M in the opposite case (MS0 is the sonic Mach number and MA0 is the Alfven Mach number). If u0 > u, the shock, although still strong, becomes almost unmodified and accelerated particle production decreases inversely proportional to u0.

Coronal Heating in Active Regions as a Function of Global Magnetic Variables

A comparison of X-ray images of the Sun and full disk magnetograms shows a correlation between the locations of the brightest X-ray emission and the locations of bipolar magnetic active regions. This correspondence has led to the generally accepted idea that magnetic fields play an essential role in heating the solar corona. To quantify the relationship between magnetic fields and coronal heating, the X-ray luminosity of many different active regions is compared with several global (integrated over entire active region) magnetic quantities. The X-ray measurements were made with the SXT Telescope on the Yohkoh spacecraft; magnetic measurements were made with the Haleakala Stokes Polarimeter at the University of Hawaii's Mees Solar Observatory. The combined data set consists of 333 vector magnetograms of active regions taken between 1991 and 1995; X-ray luminosities are derived from time averages of SXT full-frame desaturated (SFD) images of the given active region taken within ±4 hours of each magnetogram. Global magnetic quantities include the total unsigned magnetic flux Φtot ≡ ∫ dA|Bz|, B2z tot ≡ ∫ dAB2z, Jtot ≡ ∫dA|Jz|, and B2⊥,tot ≡ ∫ dAB2⊥, where Jz is the vertical current density and Bz and B⊥ are the vertical and horizontal magnetic field amplitudes, respectively. The X-ray luminosity LX is highly correlated with all of the global magnetic variables, but it is best correlated with the total unsigned magnetic flux Φtot. The correlation observed between LX and the other global magnetic variables can be explained entirely by the observed relationship between those variables and Φtot. In particular, no evidence is found that coronal heating is affected by the current variable Jtot once the observed relationship between LX and Φtot is accounted for. A fit between LX and Φtot yields the relationship LX 1.2 × 1026 ergs s-1(Φtot/1022 Mx)1.19. The observed X-ray luminosities are compared with the behavior predicted by several different coronal heating theories. The Alfven wave heating model predicts a best relationship between LX and Φtot, similar to what is found, but the observed relationship implies a heating rate greater than the model can accommodate. The Nanoflare Model of Parker predicts a best relationship between LX and B2z,tot rather than Φtot, but the level of heating predicted by the model can still be compared to the observed data. The result is that for a widely used choice of the model parameters, the nanoflare model predicts 1.5 orders of magnitude more heating than is observed. The Minimum Current Corona model of Longcope predicts a qualitative variation of LX with Φtot that agrees with what is observed, but the model makes no quantitative prediction that can be tested with the data. A comparison between LX and the magnetic energy Emag in each active region leads to a timescale that is typically 1 month, or about the lifetime of an active region, placing an important observational constraint on coronal heating models. Comparing the behavior of solar active regions with nearby active stars suggests that the relationship observed between LX and Φtot may be a fundamental one that applies over a much wider range of conditions than is seen on the Sun.

Alfven Wave Transmission and Heating of Solar Coronal Loops

We discuss the problem of wave transmission from the solar photosphere into coronal loops. We conclude that wave energy can be efficiently transmitted into loops with a sufficiently twisted magnetic field. The value of the required twist is below but close to the threshold for kink instability.

Nonthermal Velocities in the Solar Transition Zone and Corona

Nonthermal velocities are presented for spectral lines covering the temperature range 10 4–10 6 K, measured from high-spectral-resolution data for several solar features observed at the limb by the high resolution telescope and spectrograph (HRTS), including a coronal hole, ‘quiescent regions’ and several small-scale active regions. These results are compared with predictions based on acoustic waves and heating via Alfven waves. It is likely that more than one mechanism is operating simultaneously, in particular, resonant Alfven wave heating, which is very sensitive to background plasma motions.

Two-Phase Broad-Line Regions in the Presence of Alfven Wave Heating: The Role of Nonlinear and Turbulent Heating

We consider the heating caused by the damping of Alfven waves (nonlinear and turbulent) on thermal stability of a two-phase medium at broad-line cloud pressures of quasars. In particular, we investigate the distinct density dependencies of each heating mechanism in the heat-loss function. The heat-loss function contains the following physical processes: recombination, electron excitation of resonance transitions, bremsstrahlung, Compton interactions, and damping of Alfven waves. We compare the efficiencies of the Alfvenic heatings: nonlinear, resonance surface, and turbulent.