Construction Classics

Electrons in gas: focusing, absorption, range and glow

Electrons in a small accelerator rarely travel in a perfect vacuum. They leave the ion-source filament into hydrogen at a few pascals, they are shaken loose in the dee gap, and some end in a viewport. These four documents, two of them older than the cyclotron, are the measured physics of that passage: how a trace of gas can focus a beam rather than scatter it, how strongly each gas removes slow electrons from a beam, how far an electron of 10 keV and up travels and what fraction of its energy becomes X-rays, and what a kilovolt beam makes a gas glow with, and where.

Why these documents can be hosted

Johnson (1922) and Brode (1925) were published in the United States more than ninety-five years ago, so their copyright terms have expired whatever notice they originally carried. The Johnson scan is the Internet Archive’s copy of the Bell System Technical Journal article; the Brode scan is from an Internet Archive serial scan of Physical Review, and its first page is the May 1925 issue’s title page, which opens with a different paper, before Brode’s begins on p. 636. Neither carries a later publisher’s stamp or download watermark.

NASA SP-3012 is a NASA Special Publication written by two National Bureau of Standards physicists, printed from copy supplied by the contractor and sold by the Office of Technical Services of the Department of Commerce; it is a work of United States Government employees and carries no notice. One check mattered: its preface lists the twelve reports and two appendices of the NAS-NRC volume it was to form part of, and the appendices are reprints from the Annual Review of Nuclear Science. They are not in this document, which contains the Berger–Seltzer report alone, as its own contents pages and 134 pages confirm. NASA TN D-6005 is a Langley Research Center technical note marked Unclassified – Unlimited on its report documentation page.

One document from the same mining wave is cited but not hosted. JPL Technical Report 32-1500 (Woo, 1970, RF voltage breakdown in coaxial lines) was prepared by the Jet Propulsion Laboratory of the California Institute of Technology under NASA contract NAS 7-100, and its scan carries the contract line and nothing else: no statement that the work is the Government’s or that distribution is unlimited. A contractor report without such a statement is not hosted here; its eight rules link to the NTRS record. Determinations made October 2026.

Focusing a beam with gas (Johnson 1922)

Johnson’s tube at Western Electric ran at 300 to 400 volts, and its point was that a low-voltage beam could be made usable at all. In a high-vacuum tube the spot would have been 1 cm across; gas at a few thousandths of a millimetre of mercury brought it to 1 mm (dg-1964). His explanation is ion space charge: positive ions made by beam collisions drift out only at thermal speed and accumulate in the beam, and about four ions per electron supply the 1 V/cm radial field his one-degree divergence case needed; a crossed-beam test measured a field equivalent to about 3 V/cm (dg-1965).

The engineering consequences follow directly. Because the ion count scales with the beam, more current means a shorter focus, and Johnson used current, set by cathode temperature, as the focus control (dg-1966). The focus takes about a microsecond to build, so a spot swept at 10⁵ Hz stayed sharp and one swept at 10⁶ Hz widened (dg-1967). Heavy gases work and light ones barely do: focus came easily in nitrogen, argon or mercury vapour and with difficulty in hydrogen or helium, because slow heavy ions stay in the beam longer (dg-1968). He settled on argon at 5 to 10 microns (dg-1969), and kept the volume shared by cathode and anode under 1 cm³ so that no inter-electrode path was long enough for an arc to build at that pressure (dg-1970). A hydrogen ion source runs the same geometry the other way round, and that last rule is the one its designer meets first.

How strongly each gas stops slow electrons (Brode 1925)

Brode measured, for seven gases, the fraction of a beam of electrons at 2 to 360 volts that survives a known path at a known pressure. His coefficient a is defined by I = I₀ exp(−a x p) with x in centimetres and p in millimetres of mercury; its reciprocal at a given pressure is the mean free path for removal from the beam, and dividing by 3.65 × 10¹⁶ molecules per cm³ at 1 mm gives the cross-section per molecule (dg-1976). Nothing in that definition has aged.

The curves are the Ramsauer effect seen from the beam’s side, and Brode plots Ramsauer’s dotted curve beside his own. Argon is strongly selective, peaking sharply near 12 V at about a = 55 and falling to about 7 at 360 V, with the 2 V value a fifth of the peak (dg-1977). Helium has a broad maximum near 4 V at about 22 and is the most transparent of his gases at tens to hundreds of volts (dg-1978). Hydrogen has no maximum at all: a rises steadily as the energy falls, about 50 at 2 V, 10 near 36 V and 6 near 170 V, while nitrogen and carbon monoxide track each other with a maximum near 18 V and a minimum near 9 V, extremum positions Brode cautions were not determined accurately (dg-1979). The figure readings in these rules are labelled as such.

Range and radiation yield from 10 keV (NASA SP-3012)

The Berger–Seltzer tables are the printed 1964 tabulation of electron collision and radiative stopping power, continuous-slowing-down range and radiation yield, for elements and compounds from hydrogen to air. For a current number the live source is NIST’s online ESTAR tables; this volume is worth having for what it says about its own limits. The tables start at 10 keV and are least certain there: below the point where the electron velocity approaches the atomic-electron velocity the stopping-power formula ceases to be valid, so the range integral is closed by linear interpolation to zero below 1 keV, and the 10 keV ranges exceed Nelms’ earlier tabulation by 12% for lead and 1% for hydrogen, converging to within 0.5% by 50 keV (dg-1980). The authors’ own accuracy estimate puts the collision stopping power at 1–2% and the bremsstrahlung cross-sections at 20% up to 2 MeV (dg-1981).

Three table rows were read from the page images, because the scan’s text layer cannot be trusted on tabular digits. At 10 keV the collision stopping power is 17.91 MeV cm²/g in neon, 14.57 in argon and 19.70 in air; the c.s.d.a. ranges are 3.226 × 10⁻⁴, 4.050 × 10⁻⁴ and 2.892 × 10⁻⁴ g/cm²; and the radiation yields are 2.19 × 10⁻⁴, 4.425 × 10⁻⁴ and 1.463 × 10⁻⁴, argon’s being twice neon’s (dg-1982, dg-1983, dg-1984). The radiation yield is the fraction of a 10 keV electron’s energy that leaves as X-rays, which is the number the X-ray output shelf picks up.

What a keV beam makes a gas glow with (NASA TN D-6005)

Langley fired a 26 keV electron beam across a low-density helium wind tunnel to make the flow visible, then put a spectrograph on the light to find out what was glowing. The brightness tracked local gas density (dg-1971), but the spectrum was not what a pure-helium calculation would give. With 40 to 400 ppm of nitrogen in the gas, the N₂⁺ first-negative band was strong at every observation point and dominated far from the beam, at an intensity too high for direct beam excitation; the authors cite transfer from helium metastables or from He₂⁺ as the suggested mechanisms (dg-1972). Where the light came from depended on distance: atomic helium inside the beam, molecular helium just downstream, the nitrogen ion far away, with atomic lines extending several beam-core diameters and He₂ emission persisting more than 500 microseconds (dg-1973). Anyone who has watched a beam glow in a chamber and tried to read its edge from the light should read p. 11.

Two apparatus notes transfer whole. Laboratory measurements the authors quote put 15 percent of a 26 keV beam backscattered from a steel plate, and photographs with and without a collector that limited backscatter showed scattered electrons to be a significant part of the upstream excitation (dg-1974): walls light up gas far from the beam. And the gun itself, filament and cathode shield at −10 to −40 kV with the anode and drift tube at ground, was held at 2 × 10⁻⁵ to 2 × 10⁻⁴ mm Hg by a differential-pumping section of two 0.102 cm orifices with a mechanically pumped chamber between them, while the region outside ran as high as 10 mm Hg (dg-1975).

Why these four belong together

Johnson shows the gas focusing the beam; Brode measures the gas removing electrons from it; Berger and Seltzer tabulate how far the survivors go and how much of their energy comes out as X-rays; Hillard, Ocheltree and Storey show what the whole process looks like. They span 1922 to 1970 and three institutions that never worked together, and each is cited in the Design Guide for its measurements rather than its apparatus. Read them for the numbers and the definitions; the tubes, the spectrograph and the tunnel are period pieces.

Design rules extracted from these documents

21 Design Guide rules come from these four documents, spread across beam dynamics, space charge, physics theory, detectors and vacuum. Representative examples:

• dg-1964 — a trace of gas can focus a low-voltage electron beam: 1 cm spot to 1 mm at a few thousandths of a millimetre of mercury
• dg-1966 — in a gas-focused beam the focal length is set by the beam current
• dg-1968 — heavy fill gases focus far more readily than hydrogen or helium
• dg-1976 — Brode’s absorption coefficient, its reciprocal as a mean free path, and the conversion to a cross-section
• dg-1977 — argon is strongly energy-selective for slow electrons, peaking near 12 V
• dg-1980 — the electron tables start at 10 keV and are least certain there
• dg-1972 — tens of ppm of nitrogen can dominate the visible glow of an electron beam in helium
• dg-1974 — electrons backscattered from walls light up gas far from the beam

Every rule, by document:

• Johnson 1922 (7): dg-1964, dg-1965, dg-1966, dg-1967, dg-1968, dg-1969, dg-1970
• Brode 1925 (4): dg-1976, dg-1977, dg-1978, dg-1979
• NASA SP-3012 (5): dg-1980, dg-1981, dg-1982, dg-1983, dg-1984
• NASA TN D-6005 (5): dg-1971, dg-1972, dg-1973, dg-1974, dg-1975