{
  "annotation_id": "de337782-07ab-4a7d-93a4-c72d536f53f1",
  "date_created": "2026-03-02T18:00:53.631000Z",
  "date_modified": "2026-03-02T18:00:53.631000Z",
  "file_hash": "ebc44a0e6ca04ff468db0bbcadda37d8702fdf5aa1f7b86f85c85f2c62b3bf3c",
  "private": false,
  "record": {
    "abstract": "The Child-Langmuir law relates the voltage applied across a planar diode to\nthe saturation value J_CL of current density that can be transmitted through it\nin case the injection velocity of electrons into the diode is zero. The\nChild-Langmuir current density J_CL is, at the same time, (i) the maximum\ncurrent density that can be transmitted through a planar diode, (ii) the\ncurrent density below which the flow is steady and unidirectional in the long\ntime limit and (iii) the average transmitted current density for {\\em any}\nvalue of injected current density above J_CL. Existing generalizations of\nChild-Langmuir law to non-zero velocities of injection are based on the\ncharacteristics (i) and (ii) of J_CL. This paper generalizes the law to\nnon-zero velocities of injection based on the characteristic (iii) by deriving\nan analytical expression for the saturation value of current density. The\nanalytical expression for the saturation current density is found to be well\nsupported by numerical computations. A reason behind preferring the saturation\nproperty of the Child-Langmuir current density as the basis for its\ngeneralization is the importance of that property in numerical simulations of\nhigh current diode devices.",
    "arxiv_id": "physics/0411175",
    "authors": [
      "R. R. Puri",
      "Debabrata Biswas",
      "Raghwendra Kumar"
    ],
    "categories": [
      "physics.plasm-ph",
      "physics.gen-ph"
    ],
    "doi": "10.1063/1.1644583",
    "journal_ref": "Physics of Plasmas, 11 (2004) 1178",
    "title": "Generalization of Child-Langmuir Law for Non-Zero Injection Velocities   in a Planar Diode",
    "url": "https://arxiv.org/abs/physics/0411175"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b5d66fe5-4ffe-49ed-9330-352d9a1bac2c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}