## Periodic Reporting for period 2 - SoWHat (Solar Wind Heating and Turbulence)

Reporting period: 2017-11-01 to 2018-10-31

In a collisionless, magnetized plasma, particles may stream freely along magnetic-field lines, leading to ''phase mixing'' of their distribution function and consequently to smoothing out of any ''compressive'' fluctuations (of density, pressure, etc.,). This rapid mixing underlies Landau damping of these fluctuations in a quiescent plasma, one of the most fundamental physical phenomena that make plasma different from a conventional fluid. Nevertheless, broad power-law spectra of compressive fluctuations are observed in turbulent astrophysical plasmas (most vividly, in the solar wind) under conditions conducive to strong Landau damping. Elsewhere in nature, such spectra are normally associated with fluid turbulence, where energy cannot be dissipated in the inertial scale range and is therefore cascaded from large scales to small. The major objective of the project has been to explain this surprisingly fluid dynamics.

By direct numerical simulations and theoretical arguments, we have shown that turbulence of compressive fluctuations in collisionless plasmas strongly resembles one in a collisional fluid and does have broad power-law spectra. This ''fluidization'' of collisionless plasmas occurs because nonlinear advection effectively nullifies phase mixing, with free-energy fluxes in the inertial range largely confined within each moment of the distribution function, taking its energy from large to small spatial scales where it dissipates. We interpret this behavior as resulting from statistical cancellation of phase mixing by plasma echoes. These are excited, because the nonlinear advection causes phase mixing modes propagating toward smaller-velocity space scales to couple to antiphase mixing ones, propagating back to larger scales—the result is a return flux from phase space. Besides resolving the long-standing puzzle of observed compressive fluctuations in the solar wind, our results suggest a conceptual shift for understanding kinetic plasma turbulence generally: rather than being a system where Landau damping plays the role of dissipation, a collisionless plasma is effectively dissipationless except at very small scales. The universality of ''fluid'' turbulence physics is thus reaffirmed even for a kinetic, collisionless system.

Implications for modeling techniques: There is a thriving industry of effective fluid models of collisionless plasmas, of which the most sophisticated strand is the Landau fluid closures. Their underlying idea is to assume that Landau damping removes free energy from low to high Hermite moments as effectively in a nonlinear system as in a linear one. This might seem to be the exact opposite of the main conclusion of this work. However, Landau fluid models have consistently been found to work better when more—but not necessarily many more—moments are kept compared with the standard fluid approximation. It might be argued that the art of crafting a good Landau fluid model is precisely to do it in such a manner as to capture the effect of the echoes within a minimal set of Hermite moments while setting the boundary (closure) condition at the maximum retained Hermite moments so as not to introduce or divert free-energy flows in a spurious way. With the echo effect and fluidization now explicitly part of one’s intellectual vocabulary, one might hope to revisit this task with renewed vigor, purpose, and insight.

Implications for Astrophysical Theory: One cannot either adequately enumerate or indeed, anticipate all of the instances across the vast canvas of plasma astrophysics where the nature of collisionless plasma turbulence may prove to be of interest. We wish to highlight one problem that has a long history and has recently seen a burst of activity. It is a long-standing question in the theory of matter accretion onto black holes whether and to what degree plasma turbulence, which is excited in the accretion disk by instabilities driven by the Keplerian shear and helps enable accretion by transporting angular momentum, can be thermalized preferentially on ions rather than electrons or vice versa. This has implications for the relative amounts of energy radiated out by electrons (and thus, observed) vs. swallowed by the black hole as mass (ions) is sucked in as well as for observational signatures of disks and their jets. Our findings indicate that, at least at beta~1 most of the energy arrives to ions scales whiteout being dissipated. Since the theory (or even a reliable modeling prescription) of energy partition in plasma turbulence is still being developed, this is a useful factual constraint to have.

Implications for General (Plasma) Physics: The peregrinations and rearrangements of energy through a system’s phase space are a recurrent motif of theoretical physics. Turbulence theory is explicitly constructed to describe the energy’s thermalization routes, which bridge the usually vast separations between its injection and dissipation scales, producing rich, multiscale non-linear structure in the process. In weakly collisional plasmas, these energy transfer routes are in a 6D phase space, with velocity space refinement (phase mixing) of the particles’ distribution functions in general as effective as spatial mixing in accessing dissipation mechanisms. It is perhaps noteworthy that, in the case of inertial-range turbulence of a magnetized plasma, one of these forms of mixing turns out unambiguously to be the winner: spatial advection outperforms phase mixing and makes a collisionless plasma resemble a collisional fluid. Those who believe in the universality of nonlinear dynamics might be pleased by such an outcome. For plasma physicists, this is a sobering reminder that collisionless dissipation processes that make our subject so intellectually distinctive are not irreversible until they are consummated by collisional entropy production—and an intriguing demonstration that nonlinear effects can sometimes hinder them in favor of more ''fluid-like” entropy-production mechanisms.

Implications for Astrophysical Theory: One cannot either adequately enumerate or indeed, anticipate all of the instances across the vast canvas of plasma astrophysics where the nature of collisionless plasma turbulence may prove to be of interest. We wish to highlight one problem that has a long history and has recently seen a burst of activity. It is a long-standing question in the theory of matter accretion onto black holes whether and to what degree plasma turbulence, which is excited in the accretion disk by instabilities driven by the Keplerian shear and helps enable accretion by transporting angular momentum, can be thermalized preferentially on ions rather than electrons or vice versa. This has implications for the relative amounts of energy radiated out by electrons (and thus, observed) vs. swallowed by the black hole as mass (ions) is sucked in as well as for observational signatures of disks and their jets. Our findings indicate that, at least at beta~1 most of the energy arrives to ions scales whiteout being dissipated. Since the theory (or even a reliable modeling prescription) of energy partition in plasma turbulence is still being developed, this is a useful factual constraint to have.

Implications for General (Plasma) Physics: The peregrinations and rearrangements of energy through a system’s phase space are a recurrent motif of theoretical physics. Turbulence theory is explicitly constructed to describe the energy’s thermalization routes, which bridge the usually vast separations between its injection and dissipation scales, producing rich, multiscale non-linear structure in the process. In weakly collisional plasmas, these energy transfer routes are in a 6D phase space, with velocity space refinement (phase mixing) of the particles’ distribution functions in general as effective as spatial mixing in accessing dissipation mechanisms. It is perhaps noteworthy that, in the case of inertial-range turbulence of a magnetized plasma, one of these forms of mixing turns out unambiguously to be the winner: spatial advection outperforms phase mixing and makes a collisionless plasma resemble a collisional fluid. Those who believe in the universality of nonlinear dynamics might be pleased by such an outcome. For plasma physicists, this is a sobering reminder that collisionless dissipation processes that make our subject so intellectually distinctive are not irreversible until they are consummated by collisional entropy production—and an intriguing demonstration that nonlinear effects can sometimes hinder them in favor of more ''fluid-like” entropy-production mechanisms.