---
title: "Supernova Remnant Shocks and Particle Cycles Interactive Lab | Sandbox Physics"
description: "How do surrounding gas and a local field change a remnant and its energetic seeds?"
canonical_url: "https://sandboxphysics.com/labs/supernova-remnant-shocks/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/supernova-remnant-shocks/"
last_modified: "2026-11-05"
---

Two shocks and a short acceleration window

# Supernova Remnant Shocks and Particle Cycles

**How do surrounding gas and a local field change a remnant and its energetic seeds?** Fast ejecta drive a shock into surrounding gas while a reverse shock processes the ejecta. At the same age, denser surroundings make the remnant smaller and slower. Repeated scattering can raise the momentum of already energetic seeds; the short saved cycle model does not calculate their initial injection or the remnant’s radiation.

Drag the shock to change ambient density at one age. Change a local parallel field and follow the same saved mean-cycle particle record.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

This is one specified ejecta-envelope snapshot, using the own n7 spherical adiabatic double-shock solution and a fixed physical age. It is separate from the zero-ejecta Sedov benchmark and has no computed transition into the ejecta core. The three surfaces are the forward shock, contact and reverse shock; they are geometry, not X-ray brightness. Samples show only known unshocked density. No invented post-shock density gradient is filled in. A small parallel patch uses equal normal fields upstream/downstream and prescribed Bohm scattering with fluid-convected scattering centres. The field grip changes strength along that normal; it does not create an oblique shock or a global radial-field solution. Seeds are already ultrarelativistic protons. Positive expected cohorts receive the leading Bell mean log gain and downstream escape probability. Playback reads only saved mean cycles within one percent of the specified age; the gas stays fixed. There are no individual particle trajectories, thermal injection, wave growth/damping, Alfvén drift, pressure feedback, radiative loss or gamma-ray spectrum. Seed energy is external; gained energy, escaped and retained weights have explicit ledgers and a passive-work gate. A finite mean-clock/diffusion-length endpoint is not a true maximum proton energy. Finite joint corners/endpoints/withheld inputs passed the original gates; no uniform continuous-domain error theorem or real stochastic spectrum is claimed. The nonzero mean-log closure discrepancy is retained in the independent scientific reference.

Physics tutorial

## Two shocks can belong to one expanding remnant

**Background** The fastest ejecta catch the surrounding gas first. An outer shock processes that gas, while a reverse shock processes ejecta arriving from inside. A contact separates the two shocked materials.

**Why it matters** Changing the environment at the same age alters the radii and shock speed. A small local patch then lets us ask how repeated scattering changes an existing energetic seed.

Start with the essentials

- **Focus question**: Which changes come from gas dynamics, and which come from the prescribed scattering?
- **One-sentence intuition**: Density changes the fixed-age shock state. Magnetic strength changes the prescribed cycle clock. The particle model remains passive and does not move the gas snapshot.

### Core mathematical model

#### One envelope family at one age

$$
R_{\rm c}=(Ag^n/\rho_0)^{1/n}t^{(n-3)/n},\qquad n=7
$$

The unshocked envelope falls as the inverse seventh power of radius at this age; its normalization and the dimensionless coefficient are fixed. The computed forward and reverse radii are fixed multiples of the contact radius. Increasing ambient density at fixed energy, mass and age reduces all three radii.

#### Leading mean gain and escape

$$
G=\frac{4(u_1-u_2)}{3c},\qquad P=\frac{4u_2}{c},\qquad u_2=\frac{u_1}{4}
$$

Speeds are measured in the shock frame and belong to scattering centres moving with the gas. The gain is a mean log-momentum increment of a full cycle; the escape probability gives its downstream lost fraction.

#### Prescribed Bohm clock

$$
\kappa=\frac{pc}{3eB},\qquad\frac{dt}{d\ln p}=\frac{3}{u_1-u_2}\left(\frac{\kappa_1}{u_1}+\frac{\kappa_2}{u_2}\right)
$$

The field is parallel, so its normal component is equal on the two sides. Wave growth lies outside this prescription. Within it, a larger field shortens the time needed for the same log-momentum change.

#### Follow every weight and energy contribution

$$
N_{\rm ret}+N_{\rm esc}=N_0,\quad K_{\rm ret}+K_{\rm esc}=K_{\rm seed}+W_{\rm scat}
$$

External seed energy is separate from newly gained energy. Their sum is conserved exactly for the energies assigned to these mean cohorts. The physical accuracy still depends on how well that mean represents the distribution.

### Common difficulties

#### Reverse relative to which material?

**Typical misconception** A reverse shock must shrink toward the centre in the remnant-centre frame.

**Better mental model** It propagates backward relative to the freely expanding ejecta that enter it. Its radius in the remnant-centre frame can still increase. Here only the fixed instantaneous radius is shown.

#### A mean cycle is not a tracked particle

**Typical misconception** Every proton follows the displayed deterministic energy and a known spatial orbit.

**Better mental model** Positive weights represent expected cohorts with one mean-log momentum. The independent angular test retains a nonzero difference between mean energy and exponentiated mean log energy. No individual orbit or calibrated spectral width is computed.

### Run the experiment

1. 01

   #### Hold age fixed, change density

   Drag the gold point on the forward shock outward. Read the ambient density and the three surface sizes, then choose Dense gas slows the front.

   **What to observe:** At this same age, a larger radius corresponds to lower ambient density. The shaded boundaries locate the two shocks and the contact; their colors label surfaces rather than X-ray brightness.

2. 02

   #### Change the local field, not its direction

   Drag the purple arrow tip along the patch normal, or compare the weak and strong presets at the same density.

   **What to observe:** The gas radii remain the same. The prescribed scattering clock changes, so the short window can contain different numbers of complete cycles.

3. 03

   #### Calculate one baseline cycle

   For the baseline shock, use the displayed speeds to estimate the escape probability and mean log gain, then advance one saved cycle.

   **What to observe:** Both are about 0.0191. Roughly 1.91 percent of the current weight escapes, while survivors gain about 1.93 percent in representative momentum. Those are distinct changes; escaped weights keep their previous cycle momentum.

4. 04

   #### Read the saved short window

   Play the saved cycles, pause on a frame and export it. Compare retained and escaped weights, then open the energy details.

   **What to observe:** All plots and export use this accepted record and selected frame. The endpoint belongs to a short mean-clock window, not an inferred maximum energy for a remnant of this age.

Physical conclusion

At one age, ambient density sets the shock geometry. The prescribed local field then sets how quickly the energetic seeds cycle through that fixed shock.

## Related experiments and articles

Supernova remnants, two shocks and energetic seeds · Reading path

### Supernova remnants, two shocks and energetic seeds

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Why supernova remnants keep shining**](https://sandboxphysics.com/stories/supernova-remnants/why-remnants-keep-shining/)
2. [Article **How a strong shock turns motion into heat**](https://sandboxphysics.com/stories/supernova-remnants/strong-shocks-turn-motion-into-heat/)
3. [Article **Two shocks and a separate point explosion**](https://sandboxphysics.com/stories/supernova-remnants/two-shocks-and-a-point-blast/)
4. [Article **Energetic seeds gain momentum one mean cycle at a time**](https://sandboxphysics.com/stories/supernova-remnants/energetic-seeds-and-finite-acceleration/)
5. [Article **Recalculate a point blast and read the fixed HESS 2004 spectrum**](https://sandboxphysics.com/stories/supernova-remnants/replay-sedov-and-hess2004/)
6. [Article **Read the upstream X-ray hotspots before inferring a magnetic field**](https://sandboxphysics.com/stories/supernova-remnants/reading-upstream-hotspots-2026/)

Fields & matter · Starter path

## From a field to an electron microscope

Map an electric field and steer a charged particle. Then find the electron's wavelength and use electron beams to see a crystal and a surface.

[Start here → **Make an Electric Field Visible** Move the probe around a dipole and check that the field always points downhill on the potential landscape. Observe · 8 min](https://sandboxphysics.com/labs/electric-field/)

1. [1 Make an Electric Field Visible](https://sandboxphysics.com/labs/electric-field/)
2. [2 A Charge Bending through Fields](https://sandboxphysics.com/labs/charged-particle/)
3. [3 Electron Wavelength & Voltage](https://sandboxphysics.com/labs/electron-wavelength/)
4. [4 Electron Diffraction & Reciprocal Space](https://sandboxphysics.com/labs/electron-diffraction/)
5. [5 TEM Bright Field, Dark Field & SAED](https://sandboxphysics.com/labs/tem-mode-selector/)
6. [6 SEM Secondary-Electron Topography](https://sandboxphysics.com/labs/sem-topography/)

[View the full path →](https://sandboxphysics.com/topics/fields-and-matter/#starter-path)