Potential mapping method for the steady-state magnetosheath model
Abstract. We present the potential mapping method which is a model of steady-state flow velocity and magnetic field in the empirical magnetosheath domain. The method makes use of a coordinate transformation from the empirical magnetosheath domain into the parabolic magnetosheath domain, and evaluate a set of the shell variable and the connector variable to utilize the solution of Laplace equation obtained for the parabolic magnetosheath domain. Our model uses two invariants of transformation: the zenith angle in the magnetosheath and the ratio of the distance to the magnetopause to the thickness of magnetosheath along the magnetopause-normal direction. The plasma flow and magnetic field can be determined as a function of the upstream condition (flow velocity or magnetic field) in a wider range of zenith angle. The potential mapping method is computationally inexpensive by using the analytic expression as much as possible, is applicable to the planetary magnetosheath domains.
Yasuhito Narita et al.
Status: final response (author comments only)
RC1: 'Comment on angeo-2023-2', Anonymous Referee #1, 20 Feb 2023
- AC1: 'Reply on RC1', Yasuhito Narita, 06 Apr 2023
RC2: 'Comment on angeo-2023-2', Anonymous Referee #2, 20 Feb 2023
- AC2: 'Reply on RC2', Yasuhito Narita, 06 Apr 2023
Yasuhito Narita et al.
Yasuhito Narita et al.
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Referee report on 'Potential mapping method for the steady-state magnetosheath model' by Y. Narita et al.
This manuscript describes a methodology for mapping magnetosheath locations relative to specific empirically-based models for the bow shock and magnetopause into an equivalent magnetosheath location with boundaries described by confocal paraboloids. Analytic solutions for plasma streamlines (and potential) and magnetic fields (and magnetic potential) can then be conformally mapped to a space bounded by more realistic boundaries.
In general, this article does not represent a significant advancement. It reads more like an Appendix of a larger study, with the Appendix detailing a technique to map locations between confocal, parabolic boundaries and empirically-based boundaries. While this technique is similar to previous efforts as described by Soucek and Escoubet , Trattner et al., JGR , and others, there is no effort here to demonstrate that this particular mapping technique better matches observations than previous techniques.
Some of the references to empirical models of boundary shapes/sizes are inconsistent with the description provided here, or are examined under extremely specific solar wind conditions, or do not properly represent the knowledge of the physical boundaries far down the flank. Specifically,
Additional references to analytic models of the magnetosheath magnetic field (using expansions in Legendre polynomials) that make use of flexible magnetopause and bow shock boundary models (e.g., Romashets and Vandas, JGR, ) should be provided and discussed.
Although the claim is made in the manuscript that this technique can be applied to arbitrary boundary model shapes, it is not demonstrated that under general circumstances, the equations can be written in a closed form.
The technique described relies on determining the (straight line, or minimum) distance from a given point within the magnetosheath to the magnetopause. This is along the normal direction from the magnetopause. However, Lines 109-110 state that the task is to find the shell variable 'v' and the connector variable 'u' in the empirical magnetosheath. However, while the connector variable 'u' of the empirical magnetosheath is normal to the magnetopause surface, it is not a straight line through the magnetosheath – and doesn’t represent the minimum distance from the given point to the magnetopause. In other words, the distance from the magnetopause extends over a (narrow) range of connector variable 'u' values.
The rationale for the methodology described is confusing. For most implementations, the solar wind parameters are known, and the corresponding parameters at a given point within the magnetosheath are desired. However, the methodology here is to start with known parameters at a given place within the magnetosheath (relative to empirical models), conformal map to a location relative to the KF paraboloid boundaries, calculate the 'u' and 'v' values and determine the B-field, streamline, and potentials. The solar wind drivers appear to be missing. It appears that part of this strategy is based on the Toepfer et al.  motivation; but a clear description for the order of steps for this technique is missing.
Several of the equations presented are incorrect. For example, Eq.5 is infinite everywhere, due to the denominator. How are Eqs.20 and 23 are used to derive Eq.24? Why do the units not match for the terms within Eq.39? How do Eqs.31-32 lead to Eq.33 when ymp=0?