The Collision Term Set to Zero: Vlasov's Collisionless Plasma, Priced

In 1938 Anatoly Vlasov gave plasma physics the equation it still lives in: evolve the distribution function under the self-consistent collective field the particles themselves create, and set the collision integral of the Boltzmann equation to zero. I credit that paper at full strength: it founded collisionless plasma physics and on timescales short against the collisional relaxation time it is the right leading physics. Nothing in this paper falsifies the equation or a number it returns. What I evaluate is the zero's derivation status: Vlasov argues that the pair-collision picture fails for long-range Coulomb forces — an argument that the old term fails is not a derivation that its replacement is zero. My bench evaluates what the zero deletes, on declared inputs only, in entropy. At a declared two-beam state (drifts ±2.000000, beam temperature 1.000000), the entropy collisions would produce on the way to the energy-matched equilibrium is 0.638227 k_B per particle; the 1938 equation produces 0.000000 of it, forever — the flow conserves every Casimir with drifts of 0.000000. Counted plainly: 1 collision term set to zero against 0 derivations in 1938 that its replacement is zero. Grade: REASON FOUND / STILL TURNING — PREMISE-ONLY, explicitly not a kill and not a falsification. The program headline stands unmoved: vacuum catastrophe NOT SOLVED / PARTIAL, producing-count 0.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-06
DOI
https://doi.org/10.5281/zenodo.24012020
Primary Topic
Gas Dynamics and Kinetic Theory
Type
preprint
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preprint

The Collision Term Set to Zero: Vlasov's Collisionless Plasma, Priced

William Alexander Aldred
1 links
Zenodo (CERN European Organization for Nuclear Research)
Gas Dynamics and Kinetic Theory
preprint

The Collision Term Set to Zero: Vlasov's Collisionless Plasma, Priced

William Alexander Aldred
preprint en

Abstract

In 1938 Anatoly Vlasov gave plasma physics the equation it still lives in: evolve the distribution function under the self-consistent collective field the particles themselves create, and set the collision integral of the Boltzmann equation to zero. I credit that paper at full strength: it founded collisionless plasma physics and on timescales short against the collisional relaxation time it is the right leading physics. Nothing in this paper falsifies the equation or a number it returns. What I evaluate is the zero's derivation status: Vlasov argues that the pair-collision picture fails for long-range Coulomb forces — an argument that the old term fails is not a derivation that its replacement is zero. My bench evaluates what the zero deletes, on declared inputs only, in entropy. At a declared two-beam state (drifts ±2.000000, beam temperature 1.000000), the entropy collisions would produce on the way to the energy-matched equilibrium is 0.638227 k_B per particle; the 1938 equation produces 0.000000 of it, forever — the flow conserves every Casimir with drifts of 0.000000. Counted plainly: 1 collision term set to zero against 0 derivations in 1938 that its replacement is zero. Grade: REASON FOUND / STILL TURNING — PREMISE-ONLY, explicitly not a kill and not a falsification. The program headline stands unmoved: vacuum catastrophe NOT SOLVED / PARTIAL, producing-count 0.

Zenodo (CERN European Organization for Nuclear Research)
Gas Dynamics and Kinetic Theory
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