Pith Number

pith:V6KJBTV5

pith:2026:V6KJBTV5CXZDX6XPP4BCWDXCKJ

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Runaway avalanches in plasmas with external electric fields: spatially inhomogeneous case in a perturbation framework

Jie Ji, Ling-Bing He, Raphael Winter, Richard M. H\"ofer

The Landau-Coulomb system for plasmas heated by external electric fields is well-posed in a perturbative setting, with mean velocity growing linearly and temperature logarithmically while approaching a scattering Maxwellian.

arxiv:2605.14520 v1 · 2026-05-14 · math.AP

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Claims

C1strongest claim

We rigorously prove the well-posedness of the underlying nonlinear open Landau-Coulomb system in a perturbative setting and the conjectured growth bounds for the mean velocity and plasma temperature. We show that the mean velocity is linearly increasing in time, and capture the sharp logarithmic growth of the temperature. Furthermore, we prove that the electron distribution can be asymptotically described by a scattering-type Maxwellian.

C2weakest assumption

The entire analysis is performed in a perturbative setting that assumes the system remains close to a reference equilibrium with small spatial inhomogeneities; if the electric field or inhomogeneity is large, the perturbative framework and associated estimates may fail to hold.

C3one line summary

Rigorous proof of linear mean velocity increase and sharp logarithmic temperature growth for runaway electrons in the spatially inhomogeneous perturbative Landau-Coulomb equation.

References

37 extracted · 37 resolved · 0 Pith anchors

[1] Uniqueness of solutions for the non-cutoff Boltzmann equation with soft potential 2011

[2] Hajer Bahouri.Fourier analysis and nonlinear partial differential equations. Springer, 2011 2011

[3] Theory of runaway electrons in ITER: Equations, important parameters, and im- plications for mitigation 2015

[4] Physics of runaway electrons in tokamaks 2019

[5] The fluid dynamic limit of the nonlinear Boltzmann equation 1980

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:06.079720Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af9490cebd15f23bfaef7f022b0ee25265d0b3eb26e4a450a41196979ee26e60

Aliases

arxiv: 2605.14520 · arxiv_version: 2605.14520v1 · doi: 10.48550/arxiv.2605.14520 · pith_short_12: V6KJBTV5CXZD · pith_short_16: V6KJBTV5CXZDX6XP · pith_short_8: V6KJBTV5

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/V6KJBTV5CXZDX6XPP4BCWDXCKJ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: af9490cebd15f23bfaef7f022b0ee25265d0b3eb26e4a450a41196979ee26e60

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b3d189fa587253e4d336dc9225958160c0d0accd73535d67a0c2638e74f4282",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-14T08:03:40Z",
    "title_canon_sha256": "a9a9dff91a6fed2af52fd62a9ce21cd581b2b301c7b684e42893938c22d02ea8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14520",
    "kind": "arxiv",
    "version": 1
  }
}