{
  "annotation_id": "fd87645d-c45c-4439-841e-0278b6a57fe4",
  "date_created": "2026-03-02T18:00:53.180000Z",
  "date_modified": "2026-03-02T18:00:53.180000Z",
  "file_hash": "3a249eed72b66e7124cf58bfeb4c92476971c091315ba1d2904d4fd3403a8479",
  "private": false,
  "record": {
    "abstract": "There is a classic alternative to the Franck-Hertz experiment designed to\nshow more than a recurrence of the first excited state. Instead of being\nsubjected to a rising potential between source and accelerating grid, electrons\nare now accelerated in less than one excitation mean-free-path by an extra\ngrid, and then drift towards the second grid across a large equipotential\nregion. In this arrangement one must face the difficulty that the space\npotential between the grids is strongly modified by space charges. A recent\nanalysis of this experiment with mercury showed that there is a particular form\nof discharge that generates and sustains the ideal design dynamically. The\ninevitable variations of potential inside the intergrid volume are then\nconfined within a narrow sheath, a free double layer, joining two field-free\nplasma regions. The position of the double layer can be controlled so as to\noptimize the experiment. In the present paper, those phenomena are studied\ntheoretically in steady-state conditions. The essence of the method is to\nspecify velocity distributions for electrons and ions and use them to solve the\nPoisson equation. Vortex-type functions are used for trapped particles and\nmono-energetic beams for free particles. The model explains the change of\nposition of the double layer and provides a natural explanation of a threshold\ncondition for its amplitude that governs the transition between two critical\nconfigurations, in accordance with experiment. Stability and minimum\nfield-energy considerations lead to a unique solution in a four-dimensional\nparameter space where the Langmuir ratio is equal to one. The method is\nadaptable to other experiments on double layer formation under discharge\nconditions and correctly predicts the values of several plasma parameters.",
    "arxiv_id": "physics/0410126",
    "authors": [
      "Peter Nicoletopoulos"
    ],
    "categories": [
      "physics.plasm-ph"
    ],
    "title": "Theory of a stable strong electrostatic double layer generated in a   two-grid Franck-Hertz tube",
    "url": "https://arxiv.org/abs/physics/0410126"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9b665c0c-f029-428b-845f-a0ad61c21307",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}