{"id":6,"date":"2023-08-14T10:15:24","date_gmt":"2023-08-14T10:15:24","guid":{"rendered":"https:\/\/teams.issibern.ch\/collisionlessshock\/?page_id=6"},"modified":"2023-08-14T14:33:34","modified_gmt":"2023-08-14T14:33:34","slug":"sample-page","status":"publish","type":"page","link":"https:\/\/teams.issibern.ch\/collisionlessshock\/sample-page\/","title":{"rendered":"Collisionless shock as a self-regulatory system"},"content":{"rendered":"
\n

Abstract.<\/h4>\n

Collisionless shocks (CS) are one of most fundamental phenomena in
\nplasmas. The heliosphere is a natural laboratory for in situ studies of
\nthese shocks but their Mach numbers are well below that of supernova
\nremnant (SNR) shocks. With the increase of the Mach number the shock
\ntransition undergoes structural changes. We propose to consider this a
\nsequence of phase transitions. Given the upstream shock parameters, the
\nshock phase is determined by the ability of the corresponding structural
\nelements sustain stable fluxes of mass, momentum, and energy from
\nupstream to downstream. More than one microscopic process may lead to
\nthe same type of CS structure. We propose an international team
\nconsisting of specialists in heliospheric shock observations, numerical
\nsimulations, astrophysical shocks, and theory, in order to advance this
\nnovel paradigm.<\/p>\n

Background.<\/h4>\n

CS are one of most fundamental phenomena in plasmas. They are
\nencountered in all plasma environments, from a lab\u00a0 to a
\ngalaxy cluster\u00a0, and at all
\nspatial scales, from mm to kpc. SNR shocks are one of the most efficient
\naccelerators of charged particle in the universe. SNR shocks are one of
\nthe most efficient accelerators of charged particle in the
\nuniverse\u00a0. The
\nheliosphere is the only place where CS can be studied with in situ
\nmeasurements whereas these shock Mach numbers are well below those for
\nSNR shocks. Understanding SNR shocks requires knowledge of CS structure
\nat high Mach numbers. With the increase of the Mach number, the shock
\nmagnetic field profile undergoes structural changes from a nearly
\nmonotonic (MT) transition to a planar stationary (PS) profile, to
\nrippled, reforming, and possibly turbulent states, as illustrated in
\nFig.\u00a01.<\/p>\n

\"\"
\n\"\"
\n\"\"
\n\"\"
Top left: phase A – the Alfv\u00e9nic Mach number \"M_A\\approx and the
\nshock angle \"\\theta_{Bn}\\approx, the overshoot-undershoot structure, no
\nindications of non-planarity or time dependence. Top right: phase B –
\n\"M_A\\approx and
\n\"\\theta_{Bn}\\approx, multiple similar oscillations of the magnetic
\nfield are due to ripples propagating along the shock front and sweeping
\nacross the spacecraft which passes nearly tangentially through the
\nshock\u00a0. Bottom left:
\nphase C – \"M_A\\approx, \"\\theta_{Bn}\\approx, the differences in the profiles measured by four
\nCLUSTER probes (two shown) are interpreted as reformation\u00a0.
\nBottom right: phase D – \"M_A\\approx, \"\\theta_{Bn}\\approx, downstream magnetic oscillations persist and no
\nrelaxation to a uniform downstream is observed – a turbulent shock ?<\/figcaption><\/figure>\n

Understanding these structural changes is vital for understanding
\nphysics of very high Mach number shocks and, eventually, their heating
\nand accelerating efficiency. Until now this issue was not investigated
\nsystematically. Studies typically were descriptive or focused on
\npossible specific mechanisms of generation of particular features and\/or
\nparticular cases of rippling of reformation.<\/p>\n

Approach.<\/h4>\n

We suggest that a CS is a self-regulatory system, at which stable
\ntransfer of the mass, momentum, and energy, occurs from upstream to
\ndownstream, while adding coarse grained entropy. By stable we mean that
\nthere are no disruptions or substantial changes on average, except those
\nwhich are caused by variations of ambient conditions. In this approach
\nthe developing shock structure is the one which ensures this transfer.
\nThis means, that if the transfer stability is not possible without an
\novershoot, an overshoot has to be formed. If it is not possible without
\nrippling, rippling will develop, and so on. Since ions are the main
\ncarriers of these conserved quantities, it is ions which are responsible
\nfor developing the structure and it is ions which have to be most
\nstrongly affected by it. Such self-regulation has been earlier proposed
\nfor SNR shocks, in the form of a precursor adjusted to accelerated
\nparticles
\nand probably effectively reducing the Mach number relevant for the shock
\ntransition. A shock without ion reflection is in phase MT. If ion
\nreflection is significant, a shock can be in one of the phases A-D, with increased complexity of the
\nprofile. For given upstream shock parameters, the shock is in the lowest
\ncomplexity phase in which the structural elements sustain stable fluxes
\nof mass, momentum, and energy. With the increase of the Mach number,
\nwhen this stability is no longer possible, the shock experiences phase
\ntransition to the phase next in complexity. These phase transitions are
\nnot discontinuous but may be sensitive to the change of the shock
\nparameters and occur within a narrow parameter range. Ideally, phases
\nwould be separated by surfaces in the three-parameter space of \"M_A\", \"\\theta_{Bn}\", and \"\\beta\". The latter is the
\nupstream thermal-to-magnetic pressure ratio. More than one microscopic
\nprocess can lead to the transition but the phases are independent of the
\ntransition mechanism. Instead of concentrating on particular features of
\nshocks in each phase, we propose to focus on the question: given the
\nshock parameters, can we predict the phase ? Understanding the
\nconditions for such transitions would allow to make more reliable
\nconclusions about the structure of SNR shocks and the consequences of
\nthis structure, to be compared with observations.<\/p>\n

Methodology.<\/h4>\n

The approach dictates modus operandi: we will analyze whether certain
\ntypes of shock structures are able to ensure stable mass, momentum, and
\nenergy transfer in a selected range of shock parameters. Specifically,
\nwe explore the conservation laws for mass and momentum<\/p>\n

\"\\frac{\\partial<\/p>\n

\"\\frac{\\partial<\/p>\n

and similarly for energy. Here \"i,j=x,y,z\", where \"x\" is along the shock normal, and the
\nhydrodynamical variables are the moments of the distribution
\nfunction.<\/p>\n

In planar stationary shocks (phase A) only dependence on \"x\" survives. Note that phase A refers to
\nshocks with an overshoot in which ion reflection is significant. It is
\nknown that overshoots are present even in low-Mach number shocks without
\nion reflection\u00a0.
\nThis may be used as an additional signature of phase A. Rippling (phase
\nB) would introduce quasi-periodicity in space and time\u00a0. Reformation
\n(phase C) would change the behavior to impulsive\u00a0.
\nFor turbulent shocks (phase D) the above relations should be modified to
\naccount for the turbulent fields by proper averaging. The phase D may be
\nespecially relevant for SNR shocks where observations imply large
\nmagnetic field fluctuations. Observations will first provide the
\nmagnetic field profile and an estimate of the basic shock parameters,
\nused in subsequent shock modeling, test particle analysis (TPA), and
\nnumerical simulations. Based on the assumption about an observed shock
\nphase we model the shock profile and trace ions throughout. Models for
\nphase A\u00a0,
\nphase B\u00a0, and phase
\nC\u00a0 have been already
\nproposed and tested. For phase B and higher a numerical simulation may
\nbe first performed to [reduce the parameter space to properly choose the
\nparameters for TPA. The distributions, found numerically in TPA, will be
\nused to calculate the density, pressure tensor, and energy density.
\nUsing the conditions of the flux constancy, we will derive the magnetic
\nfield which is consistent with these conditions. The work will be done
\nby going up in complexity, starting with the transition into phase A. If
\nthe derived magnetic field differs substantially from the initial one,
\nwe switch to the phase B model and perform the same analysis. Upon
\nreaching satisfactory agreement, we come back to performing
\nself-consistent simulation which will provide detailed particle
\ndistributions all across the shock. The test-particle stage is important
\nsince it is not possible to incorporate measured fields in
\nself-consistent simulations. Once there is agreement between the two
\nstages, we will compare the fields and distributions, derived in both,
\nwith the fields and distributions obtained in the observations. In
\naddition, the conservation laws will be directly checked with the
\nobservational data. Expertise in SNR shock observations and theory is
\nnecessary at all stages to guide the analysis and understand what is
\nrelevant for SNR shocks.<\/p>\n

In all cases we strive to determine the limits of the parameter range
\nfor each phase. The proposed research will mainly focus on the
\ntransition to phase A and from A to B. The transition B-C will be
\ntreated in the end. Phase D has not been studied so far in the
\nheliospheric shocks. It will be devoted special attention in connection
\nwith the SNR shock observations. Whenever possible, analytical treatment
\nwill supplement the three-stage procedure (observation, test particle
\nanalysis, simulation).<\/p>\n

Impact.<\/h4>\n

We propose a novel approach which is expected to significantly affect
\nfurther studies of collisionless shocks by applying the reasoning,
\ntypical for MHD and astrophysical shocks, to the shock structure. This
\napproach bridges over the microscopic and macroscopic features at the
\nscale of the shock transition, and also the heliospheric and
\nastrophysical shock treatment.<\/p>\n

\n