Models

grplinst implements several effective plasma-instability prescriptions from the literature. Each one is a subclass of PlasmaInstability and provides a single function —- the cooling time (\(\tau\)) —- which the base class turns into an energy loss. For details, see Physics Background §3. Because they share the same interface, most of the models are interchangeable: swap one class for another and rerun.

Notation

Every formula below is written in terms of the following scaled variables, so the numbers match the source code directly. \(\tau\) is in seconds.

Symbol	Definition
\(\tilde{E}\)	particle energy \(E / \mathrm{TeV}\) (local frame, \(E = E_\mathrm{obs}(1+z)\))
\(\tilde{n}_b\)	beam density \(n_b / 10^{-16}\,\mathrm{m^{-3}}\) (from the Flow)
\(\tilde{n}\)	ambient density \(n / 0.1\,\mathrm{m^{-3}}\) (from the MediumDensity)
\(\tilde{T}\)	ambient temperature \(T / 10^{4}\,\mathrm{K}\) (from the MediumTemperature)

A model uses only the inputs that appear in its formula; the others may be omitted (pass any placeholder object). Several models are piecewise, switching between a weak/linear branch and a saturated branch at a critical beam density \(n_\mathrm{crit}\).

Implemented prescriptions

• PlasmaInstabilityBret2010TwoStream
• PlasmaInstabilityBret2010Filamentation
• PlasmaInstabilityBroderick2012
• PlasmaInstabilityMiniati2013
• PlasmaInstabilitySironi2014
• PlasmaInstabilitySchlickeiser2012
• PlasmaInstabilityVafin2018
• PlasmaInstabilityShalaby2020

These models generally provide a cooling term (\(\mathrm{d}E / \mathrm{d}x\)). For details, see the grplinst paer.

Control parameters

Every model inherits two practical knobs from the base class, both optional constructor arguments:

• efficiency (\(\eta\), defaults to 1): multiplies the energy-loss rate; clamped to \([0, 1]\) — negative values become 0, values above 1 become 1 (a warning is logged). Set to 0 to disable the instability, or to a fraction to test sensitivity.
• limit (defaults to 0.1): the next propagation step is restricted to this fraction of the local energy-loss length, so short cooling times are resolved.

  plinst = PlasmaInstabilityVafin2018(beam, density, temperature, 0.3, 0.05) # 30% efficiency, tighter step control
  

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For the papers behind each model, see References.
For CRPropa integration, continue with Usage.