FG2. GGCM Modules and Methods

Co-chairs: John Dorelli (john<dot>dorelli<at>unh<dot>edu) and Michael Shay (shay<at>udel<dot>edu)

Goals

The overarching goal of this focus group is to understand the physics of collisionless magnetic reconnection on magnetospheric length scales (100-1000 ion inertial lengths). To this end, we have identified several broad questions (and a number of specific sub-questions) to be addressed by the focus group:

• Q1: Can global resistive magnetohydrodynamics (MHD) codes accurately model magnetospheric reconnection?
  • Q1.1: What is the effective Lundquist number of the magnetosphere? (What is the role of anomalous resistivity? Can anomalous resistivity be accurately modeled in resistive MHD codes? What are the roles of the post-MHD terms in the Generalized Ohm's Law?)
  • Q1.2: How does the physics of reconnection depend on the ad hoc resistivity model used in global MHD codes? (How does reconnection scale with resistivity in the high Lundquist number limit? What is the effect of numerical resistivity? Can we reproduce Petschek reconnection by localizing the plasma resistivity? What is the effect of current dependent resistivity?)
  • Q1.3: How does dayside magnetopause reconnection work in global MHD codes? (Is reconnection locally controlled or externally driven? Does the Cassak-Shay formula apply to the dayside magnetopause? What can resistive MHD tell us about the generation and topology of Flux Transfer Events (FTEs)?)
  • Q1.4: How does magnetotail reconnection work in global MHD codes? (Can global resistive MHD codes accurately model magnetic storms and substorms? How do simulated storms and substorms depend on the resistivity models used in resistive MHD codes?)
• Q2: How does the physics of collisionless reconnection observed in Particle-In-Cell (PIC) simulations scale up to reality?
  • Q2.1: How does the reconnection rate scale with the electron inertial length? (Does the Hall effect render the collisionless reconnection rate independent of electron mass? Is the collisionless reconnection rate universally Alfvenic?)
  • Q2.2: How does the reconnection rate scale with the ion inertial length? (Does the Hall effect render the collisionless reconnection rate independent of the ion inertial length? What is the role of magnetic flux pileup in collisionless reconnection?)
  • Q2.3: What determines the aspect ratio of the electron diffusion region in open boundary condition PIC simultions? (Are macroscopic current sheets possible in collisionless reconnection? What determines the length of the electron diffusion region in collisionless reconnection? What is the role of secondary island formation in the determination of the length of the electron diffusion region? What impact does secondary island formation have on the reconnection rate?)
  • Q2.4: Is the Hall effect necessary to produce fast collisionless reconnection? (How does fast reconnection work in electron-positron plasmas? Is fast reconnection possible in so-called "Hall-less" hybrid codes?)
  • Q2.5: What is the role of dispersive waves in the physics of fast collisionless reconnection?
• Q3: Can we extend global resistive MHD to include microscale physics which is needed to accurately model reconnection?
  • Q3.1: What is the status of global Hall MHD modeling? (What are the most robust numerical approaches? Should we go fully implicit? Semi-implicit? What about Godunov approaches? How do we handle Adaptive Mesh Refinement (AMR)?)
  • Q3.2: What is the status of global hybrid codes? (What is the role of the Hall effect in a global 3D context? How does the reconnection rate in global hybrid codes depend on the resistivity model?)
  • Q3.3: What is the status of "embedding" approaches, in which kinetic physics is added locally to an MHD code (either via code coupling or via local modification of the equations)? (What are the most important code coupling issues? Is it even possible to couple an MHD code with a PIC code? Is the region of MHD breakdown in a global MHD code sufficiently localized to make embedding computationally feasible?)

The three questions Q1-Q3 are motivated by a currently popular approach to GGCM development known as the MHD spine approach. In the MHD spine approach, a global MHD model is used as the underlying computational "spine" of the GGCM, with non-MHD physics added (e.g., via coupling with another code) in regions of the simulation domain where the MHD approximation breaks down. While this approach seems to be yielding improvements in modeling of the inner magnetosphere (e.g., several kinetic models of the ring current are being successfully coupled to global MHD codes), the important problem of collisionless reconnection -- likely the ultimate driver of magnetospheric activity -- has received little attention in the context of GGCM development.

2008 Summer Workshop

Wednesday, June 25, 1:30-3:00

• Michael Hesse -- Michael Hesse's talk addressed question Q2.3: What determines the aspect ratio of the electron diffusion region in open BC PIC simulations? In previous studies, the electron diffusion region was identified as the region where the electron frozen flux condition is violated. That is, the electron diffusion region was identified as the region where there are significant corrections to the UxB and Hall electric fields. Such an identification seems to imply that the aspect of the electron diffusion region is larger than that found in earlier PIC simulations (which used periodic boundary conditions). Hesse pointed out, however, that particles are actually losing energy (with the electron fluid simply drifting diamagnetically) to the electromagnetic fields throughout most of this large diffusion region. If one defines the electron diffusion region to be that region where particles gain energy from the fields (i.e., the dot product of current density and electric field is positive), then the electron diffusion region is much smaller.
• Kittipat Malakit -- Kittipat Malakit's addressed question Q2.4: Is the Hall effect necessary to produce fast reconnection? Malakit's work was motivated by recent so-called "Hall-less" hybrid simulations (in which the Hall term in Ohm's law is turned off), carried out by Homa Karimabadi, which seemed to demonstrate that fast reconnection was possible even in the absence of the Hall electric field. In his talk, Malakit provided a counterexample, demonstrating that in the case of reconnection of a double Harris sheet, turning off the Hall term effectively turns off fast reconnection (producing long Sweet-Parker-like current sheets).
• Mikhail Sitnov -- Mikhail Sitnov, using an open BC version of the P3D code [Zeiler et al., 2002] that was modified by Divin et al. [GRL, 34, L09109, 2007], addressed the possible role of the ion tearing mode in producing secondary magnetic islands obsevered in open BC PIC simulations (thus potentially addressing questions Q2.1-Q2.5). Sitnov noted that the code differs from Bill Daughton's both in the particle part (maintaining continuity of only the two first moments at the boundary) and in the field part (eliminating any Bz change at the x-boundaries, mimicking magnetopause reconnection). Sitnov argued that in periodic BC PIC simulations, there are no "passing" electron orbits (i.e., electrons which leave the system, a population which is essential to the development of the ion tearing mode). Sitnov argued that open BC simulations allow for the existence of such passing orbits and, thus, the ion tearing mode may be responsible for secondary island generation in open BC PIC simulations. The effect of passing electrons suggests that the reconnection onset conditions in the magnetotail may be essentially non-local. Specifically, to be tearing- or reconnection-unstable, the tail current sheet not only must be thin enough (of the order of the ion gyroradius, to provide ion dissipation), but must also be sufficiently long to provide a sufficient number of passing electorns. There was some debate among focus group participant about the relevance of ion tearing in the secondary island generation process.
• Christopher Russell -- Chris Russell presented an interesting statistical analysis of "reconnection efficiency" -- as measured by the ratio of the variation in geomagnetic activity to the variation in the z component of the Interplanetary Magnetic Field (IMF) -- at Earth's dayside magnetopause. Two results of this study were relevant to question Q1.3: How does dayside magnetopause reconnection work in global MHD codes? First, the dependence of reconnection efficiency on IMF clock angle is not as abrupt as one would expect from a simple "half-wave" rectifier model. Russell interpreted this result to mean that reconnection at a particular location on the magnetopause may depend sensitively on the local magnetic shear across the magnetopause; nevertheless, reconnection occurs simultaneously at multiple locations on the magnetopause, so that the integrated effect on geomagnetic activity may show a more gradual dependence on the IMF clock angle. Secondly, there was a dependence of reconnection efficiency on solar wind Mach number, suggesting that the solar wind exerts some control over the reconnection rate.
• Joachim Birn -- Joachim Birn substituted for Joe Borovsky, who could not attend the meeting. Borovsky addressed question Q1.3: How does dayside magnetopause reconnection work in global MHD codes? Essentially, Borovsky argued that under pure southward IMF conditions in the BATSRUS code, the subsolar magnetopause reconnection electric field is well predicted by the Cassak-Shay formula. Borovsky went on to derive a solar wind-magnetosphere coupling function, using the Cassak-Shay formula as a starting point. Borovsky further argued, based on the agreement between the Cassak-Shay prediction with the simulated reconnection electric field, that reconnection is controlled by local plasma parameters and not "driven by" (which, for Borovsky, means "matched to") the solar wind electric field. Borovsky presents three pieces of evidence for this (from BATSRUS simulations): 1) reconnection rate doesn't "match" the solar wind electric field (it's more consistent with the Cassak-Shay formula), 2) magnetic flux pileup doesn't depend on the IMF clock angle, 3) a "plasmasphere" effect was observed, in which the reconnection electric field was observed to drop as a plasmaspheric density plume arrived at the dayside magnetopause.
• Paul Cassak -- Paul Cassak presented his latest results on asymmetric reconnection, extending previous resistive MHD work to the collisionless regime. Using conservation laws, Cassak derived an analytic expression for the reconnection electric field in a two-dimensional, steady state, asymmetric (i.e., different densities and magnetic field strengths on either side of the current sheet). The resulting "Cassak-Shay" formula (see the Joachim Birn talk above) predicts that the reconnection electric field depends only on the upstream and downstream plasma mass densities and magnetic field strengths. The Cassak-Shay formula predicts that when the plasma resistivity is constant, the reconnection electric field scales like the square root of the resistivity. Thus, the Cassak-Shay provides a potential answers to questions Q1.2 and Q1.3.

Wednesday, June 25, 3:30-5:00

• John Dorelli -- John Dorelli presented a critique of the application, by Joe Borovsky, of the Cassak-Shay formula to the dayside magnetopause. In this talk, I addressed questions Q1.2 and Q1.3, arguing that: 1) magnetopause reconnection is "driven by" the solar wind in the usual sense: the solar wind electric field imposes a constraint on the local reconnection electric field such that local conditions adjust to accommodate the imposed external electric field. In 2D, this implies a matching of the solar wind electric field to the magnetopause electric field. In 3D, however, imposing zero curl on the electric field (steady state) does not imply such an exact matching; therefore, Borovsky's observation that the BATSRUS magnetopause reconnection electric field does not "match" the solar wind electric field does not imply that reconnection is controlled by local plasma parameters, as Borovsky argues. 2) when the plasma resistivity is constant, reconnection occurs via a flux pileup mechanism such that a) the amount of magnetic energy pileup is independent of the IMF clock angle (consistent with Borovsky's BATSRUS observations), and b) the reconnection electric field scales like the fourth root of the plasma resistivity (which contradicts the Cassak-Shay formula). Dorelli concluded by deriving an analytic expression (based on the Sonnerup-Priest 3D stagnation flow equations) for the flux pileup reconnection electric field at the dayside magnetopause. Dorelli further suggested that a simple way to test Cassak-Shay vs. the Sonnerup-Priest electric fields would be to look at the dependence of the reconnection electric field on the plasma resistivity: Cassak-Shay predicts a square root dependence; Sonnerup-Priest predicts a fourth root dependence.
• Masha Kuznetsova -- Masha Kuznetsova presented results which addressed the effects of collisionless physics on magnetotail dynamics (specifically, substorm onset and expansion), thus addressing questions Q1.4 (How does magnetotail reconnection work?) and Q3.3 (What is the status of "embedding approaches," in which kinetic physics is added locally to an MHD code (either via code coupling or via local modification of the equations)). Kuznetsova used analytic expressions for the nongyrotropic corrections to the electron pressure tensor to locally modify the resistive MHD Ohm's law in the BATSRUS code. These modifications result in a collapse of the Sweet-Parker current sheet to microscopic size (of the order of the ion gyroradius) as well as a dramatic increase in the reconnection rate (consistent with fast reconnection observed in PIC simulations).
• Amitava Bhattacharjee -- Amitava Bhattacharjee presented results from Hall MHD simulations (in which constant resistivity, hyper-resistivity and/or electron inertia break the frozin flux theorem), addressing question Q2.3 (What determines the aspect ratio of the electron diffusion region in collisionless reconnectio?). Bhattacharjee presented a critique of recent analytic work by Luis Chacon in which Chacon argues that extended electron current sheets are possible in electron MHD. According to Bhattacharjee, Chacon's analysis neglected a term which should not have been neglected (need further details here).
• Vadim Roytershteyn -- Vadim Roytershteyn presented new large-scale PIC simulations in collaboration with Bill Daughton & Homa Karimabadi. The main points of the presentation were:

1. These PIC simulations were NOT with open boundary conditions - but rather with two standard periodic test problems (1) single Harris and (2) double Harris sheet. We realize that the open boundary model is somewhat complicated and controversial, so our approach in this study was to fall back to very simple boundary conditions and use brute force to make the system size large enough to give the layer a chance to develop over longer time scales.
2. Both of these periodic test problems were worked with two completely different PIC codes (NPIC vs VPIC) that use very different numerical methods. However, the results from these two codes are in excellent agreement on the question of electron sheet elongation + secondary island formation.
3. We furthermore used both of our PIC codes to work exactly the same double Harris sheet problems as the recent PRL by Shay et al. Both of our PIC codes show multiple secondary island formation (even at late time) in clear contradiction to the results obtained by Shay et al. Furthermore, the reconnection rate in our PIC simulations is modulated in time with the length of the electron layer, while the results from Shay are "steady". This is not a matter of a "different interpretation". The simulation results are clearly different. We welcome further comparisons from anyone in the community who is interested in resolving this discrepancy. It would seem crucial to understand these very real code differences, in order to move forward on the "role" of secondary islands.
4. Secondary-island formation cannot be the whole story - but we believe it clearly offers one mechanism to control the length of the electron layer. The fact that reconnection rates are similar to Hall MHD does not prove the physics is the same - especially when the time-dependence and macroscopic structure are quite different. Kinetic simulations of pair plasma (mi=me) gives precisely this rate, even in small systems where there are no plasmoids and no Weibel instability. Two-fluid simulations of pair plasma have also demonstrated this same rate without plasmoids or Weibel [Chacon, PRL, 2008].

• Brian Sullivan -- Brian Sullivan presented results from 3D resistive Hall MHD simulations of driven reconnection. Starting from a double Harris sheet equilibrium, reconnection was driven by a three-dimensionally localized inflow. Thus, a three-dimensional stagnation flow was produced, making this study relevant to Earth's dayside magnetopause. Thus, this study addressed questions Q1.3 (How does dayside magnetopause reconnection work in global MHD codes?). An attempt was made to define and identify a three-dimensional "magnetic island" and determine the dependence of the reconnection rate on the aspect ration of the dissipation region. Interestingly, the three-dimensional nature of the forcing function resulted in the addition of a "geometrical factor" (resulting from the fact that plasma flows out in all directions downstream of the reconnection current sheet) to the familiar two-dimensional expression.