# RMO90 — physical questions, source checks and the limits of a similarity test 6 September 2026. Continuation of RMO89. This is an explanatory and dimensional audit; the existing solver and scientific outputs are unchanged. ## Result in one sentence Blast/piston describes the driving history, fast/slow describes a local MHD family, and self-similarity describes a special form of evolution; a necessary magnetic scaling test passes for a 1/r field in the specified cylindrical reference scaling, but no full magnetic blast has been calculated here. ## The explanation, in order 1. Start with two uniform plasma regions separated by a boundary. Their density, pressure, velocity and field may differ. 2. One moving jump cannot generally connect arbitrary states consistently with every conservation law. Several waves and intermediate states may be needed. 3. Their different propagation speeds spread their trajectories apart in a position–time diagram. This is the Riemann fan. It need not resemble the shape of a feature in an EUV image. 4. Self-similarity is a special evolution in which rescaled profiles keep their shape. A blast uses distance divided by its current radius, with the necessary amplitude scales. A scale-free planar Riemann solution uses x/t. 5. Neither name specifies the driver. A fast shock can be maintained by a piston or propagate after the driver has ceased to supply appreciable work. 6. A global expansion model can supply a local state pair for RMO, but the local checks do not themselves verify that global model or identify the observed feature. The browser contains the same comparison, explanatory steps and links to the preserved contact and Brio–Wu examples. ## Source audit | Primary source | What was checked | Evidence limit | | --- | --- | --- | | [Takahashi & Yamada (2013)](https://arxiv.org/pdf/1210.5584), §§2–3 | Planar constant initial states, self-similar waves/discontinuities, characteristic families and non-regular possibilities | This establishes the framework, not completeness of the RMO saved examples. Full author manuscript consulted. | | [Nindos et al. (2011)](https://arxiv.org/html/1105.1268v1), introduction and event discussion | Distinction between blast and piston interpretations; temporary driving followed by propagation | Used for the physical distinction, not as an automatic rule for any RMO event. Author manuscript consulted. | | [Greifinger & Cole (1962)](https://doi.org/10.1063/1.1706571), authored abstract, plus [RAND report record](https://www.rand.org/pubs/research_memoranda/RM3054.html) | Cylindrical hydrodynamically strong shock; ideal gas and infinite conductivity; azimuthal field of a line current; external circuit maintaining current | Publisher/author-abstract information and report metadata were accessible. The complete 44-page report and its boundary-value equations were not reproduced or independently solved in this checkpoint. | The Greifinger–Cole geometry is **azimuthal**, not an unspecified or automatically uniform axial field. Constant external current is a boundary condition with an energy-budget consequence. The RAND landing page alone does not document every field assumption; the authored abstract, also indexed in the [OSTI record](https://www.osti.gov/biblio/4740466), provides those details. No copyrighted article or figure is redistributed. ## Necessary scaling check — derivation in this audit This calculation tests compatibility of exponents. It is not an ODE solution, an existence proof, a solar fit or a reproduction of Greifinger–Cole. Let the cylindrical shock radius be R proportional to t^α, its speed D = dR/dt, ambient density proportional to r^(−ω), and the magnitude of the relevant transverse ambient field proportional to r^(−m). Assume constant permeability. If a magnetic stress has a finite nonzero role in a one-coordinate similarity ansatz, the shock-boundary ratio \[ Q_B=\frac{B(R)^2}{\mu_0\rho(R)D^2} \] must be time independent. Its exponent is \[ q=\alpha(\omega-2m-2)+2. \] This ratio is magnetic-to-inertial **stress**, using B²/μ0. Magnetic pressure is B²/(2μ0); the factor two does not alter the exponent. As a separate reference, a cold, fixed-energy-per-unit-length cylindrical blast with finite dimensionless energy integral has energy scale ρ(R) R² D². Constancy gives \[ \alpha(4-\omega)-2=0. \] For uniform density, this reference exponent is α = 1/2. Then q = 1 − m. A 1/r field (m = 1) passes the magnetic-ratio scaling condition. For a uniform field (m = 0), Q_B grows proportional to t: the same fixed-energy reference scaling cannot keep a finite magnetic contribution unchanged. An independent ratio calculation illustrates the exponents without fitting any plasma data. Between t and 4t, this reference radius doubles and D halves. The density stays constant. If B decreases as 1/R it halves, so Q_B is unchanged. If B is uniform, Q_B increases by four. These are dimensionless ratio controls, not synthetic solar measurements. The uniform-field control can be regarded as an axial field transverse to the local radial normal. It is not the azimuthal line-current configuration. A spatially uniform azimuthal magnitude would require a separate ambient force-balance analysis and is not assumed here. The passing 1/r slope matches the exterior field of a constant line current. This is only a necessary compatibility observation. The fixed-energy reference derivation **does not assert a conserved total disturbance energy in the Greifinger–Cole externally maintained circuit**. A full calculation must define the energy supplied by that circuit, the singular/inner region, ambient balance, divergence-free field, shock jump and inner boundary conditions. Other field profiles, driving laws or asymptotic regimes can have other similarity constructions; this check rules out only the particular finite-field ansatz stated above. `physical_questions/scaling_check.py` records exact rational exponents and independent direct time-ratio controls in `RMO_similarity_scaling_check.json`. It runs no PDE or nonlinear boundary-value solver. ## What can be connected to RMO next? An explicitly selected global model would have to provide physical ρ, p, velocity and magnetic field immediately before and after one patch, a common normal component of B, and the front normal and speed in a specified frame. With these, local RH, entropy and characteristic checks can be applied. The local thin-front jump conditions also apply to a curved front using its local normal; a planar global fan is an additional idealisation. The current perpendicular solar reconstruction is a local finite-strength shock model. It does not supply the whole blast profile, an energy-release history or the line-current boundary conditions. Hydrodynamically strong asymptotics must not be assumed merely because a front was called a shock. Remaining work for a particular magnetic blast benchmark: obtain and read the full formulation; specify its complete energy and boundary conditions; reproduce the profiles and reference values; extract and independently check its local jumps; compare a selected solar patch with corresponding model observables. These are dependencies, not completed results or a newly authorised global numerical campaign. ## Preservation and delivery The new browser section uses existing native disclosure/navigation behaviour. Old explanatory text, figures, inputs, downloads, scripts and numerical records are retained. No driver classifier or blast solver is added. Native Chrome rendering and download acceptance are not inferred from static checks.