Langmuir-Irving · Source catalogue

Physical Review 33, Feb 1929, pp.195ff. The paper has a theory part and an experimental part. It is motivated by Langmuir's electron-scattering anomaly in low-pressure mercury arcs: many primary electrons gain more energy than the total tube voltage drop, and the authors suspect oscillations are the cause. Theory (Gaussian units, frequencies in cycles/s): (1) 'plasma-electron' oscillations, with positive ions as a rigid jelly and the electrons displaced, give nu_e = (n e^2/(pi m))^(1/2) = 8980 n^(1/2) Hz. For n = 1e10 cm^-3 this is 9.0e8 Hz (33 cm in air). The paper repeats the derivation with Maxwell's equations by a method credited to J. J. Thomson. It gives nu^2 = n e^2/(pi m) + c^2/lambda^2 for electromagnetic waves, and states that plasma-electron oscillations have zero group velocity. (2) 'Plasma-ion' oscillations, with Boltzmann-distributed electrons and moving ions, give nu = [n e^2/(pi m_p + n e^2 m_p lambda^2/(k T_e))]^(1/2). At short wavelengths this tends to the ion plasma frequency (about 1.5e6 Hz for Hg+ at n = 1e10). At long wavelengths it becomes 'electric sound waves' with v = (k T_e/m_p)^(1/2), about 6.5e4 cm/s for Hg+ at Te = 1e4 K. The transition lies near wavelength 2*sqrt2*pi*lambda_D, where lambda_D is the Debye-Hueckel length (k T_e/(8 pi n e^2))^(1/2), about 0.005 cm in the example. Orders of magnitude: displacing all electrons one spacing (4.6e-4 cm at n = 1e10) gives about 8.3 V/cm and 3.0e-5 erg/cm^3. Experiment: Hg-vapour arcs with tungsten filament cathodes in an 18 cm bulb, two tubes, Hg appendix temperature controlling vapour pressure. Oscillations were detected with a zincite-tellurium crystal detector and galvanometer (calibrated at 60 Hz), and frequencies were found from Lecher-wire wavelengths. Oscillations occur from 1e7 to 1e9 Hz as 'electrical noise' with no sharp resonance. Three ranges are reported: 1-100, 100-300 and 300-1000 MHz. In the 100-300 MHz range, a critical oscillation at 25 mA emission and 62.7 V anode voltage was temperature-sensitive: 263 MHz at 19 C, 231 at 20 C, 250 at 21 C, and absent below 19 C or above 21 C. A 115 MHz wave appeared on the collectors. It disappeared and a 730 MHz wave appeared when a magnetic field deflected the electrons. Position-dependent amplitude and a two-electrode interference test (>180 degrees phase change) were interpreted as wave behaviour. For the 300+ MHz range, amplitude and frequency were independent of collector potential over the whole range explored, from -80 V with respect to the cathode to 5 V above anode potential [read: p.13] (not -80 to +5 V); reversing the filament heating current changed neither frequency nor amplitude, in contrast to the 115 and 230 MHz waves, which it stopped. Frequency depended on which filament was the cathode (810 vs 880 MHz). Thirteen of 15 observed wavelengths followed a -1/2 slope against relative ionization, as eq. (6) predicts (see the Fig. 10 digitisation below). At 20 mA and 27 V the arc showed two stable states (high or low scattering) with frequencies 1080 MHz (low scattering, 26 V anode) and 660 MHz (high scattering, 28 V anode); ratio 1.64, which the authors call 'almost twice' [read: p.14], switchable with a magnet or by voltage history. In the low-frequency range, a 55 MHz oscillation with a Doppler-type argument gave a 14 cm wavelength (compared with the 18 cm bulb), and a tuned circuit located a resonance at 1.38 MHz (25 mA, 63 V), near the predicted ion limit of about 1.5 MHz. A tuned amplifier showed a continuous spectrum rather than one line. A cylindrical tube with axial filament is proposed for future work. The beam-oscillation identification is called problematic: the 115 MHz frequency fits beam oscillations, but it varied 10% for a 60% emission increase where 26% was predicted. The authors also note transit time and period inconsistencies. The deep read checked the theory section: algebra and every numerical example check, apart from two misprints. The screening exponent is printed exp(r/lambda_D) and should be exp(-r/lambda_D). The first occurrence of 2(2 pi)^(1/2) lambda_D on p.7 should be 2*sqrt2*pi*lambda_D, and the numbers use the correct form. Eq. (1) has an unstated sign convention (delta n is the electron deficit). The digest's 'epsilon' in the formulas, 'c^2 k^2', '(R T/m)' and '4.6e-5 cm' are OCR or digest artifacts. The printed forms have no epsilon, c^2/lambda^2, kT_e/m_p and 4.6e-4 cm. QE REMEDIATION ADDITIONS (2026-10-04). (A) Abstract against body. The abstract (p.1) says 'Another observed frequency of 50 to 60 megacycles may correspond to oscillations of the beam electrons', calls the correlation 'tentative until simpler experimental conditions can be attained', and says 'the theory offers no explanation of the cause of the observed oscillations'. The body (p.16) concludes 'it seems to be impossible to identify the 55 with the theoretical 18 megacycle oscillation' (period 5.5e-8 s against 2.8e-8 s transit time for a 14 cm wavelength; H. M. Mott-Smith Jr.'s theory of infinite plane trains gives nu_p as the minimum frequency a stationary observer sees). The abstract was evidently not updated after the Doppler argument failed [read: pp.1, 15-16]. (B) Small amplitude, admitted by the authors: 'although their voltage-amplitude appears to be very small we believe that they play a fundamental role in high current gaseous discharges' [read: p.2]. Crystal voltages reported: about 9 mV (p.10), 30-50 mV (p.11), about 90 mV (p.16; the 1.38 MHz line, found with a 2 mH coil at practically the condition for the 230 or 115 MHz oscillation, rechecked with a Radiola 17 broadcast amplifier, 550-1450 kc). Amplitudes in different runs differ 'several times' and the crystal may behave 'as if a frequency conversion factor for the crystal varied from time to time or with the crystal setting' [read: p.10], so amplitude comparisons between runs are unreliable. Authors: frequencies higher than 1.38 MHz 'were not sought with an amplifier'. Between 26 and 42 V anode there were oscillations of about 90 mV whose wavelengths could not be found [read: pp.11-16]. (C) Thermal-electron argument (pp.5-6, deep read). Fast thermal electrons cross a local disturbance in less than a cycle and do not count in the effective density n; slow ones do. So n depends on wavelength, 'this will give rise to a decrease of frequency with decreasing wave-length', and the fall in frequency lowers the effective density further, 'a kind of cumulative action which may make oscillations below a certain minimum size impossible'. 'Some calculations which we have made' support it but no quantitative treatment is given [read: p.6]. Predicted sign d(nu)/d(lambda) > 0. Later Bohm-Gross dispersion has the opposite sign (frequency rises as wavelength falls) [memory, high]; the 'minimum size' falls where Landau damping becomes strong, lambda about 2 pi lambda_De = 0.043 cm at the paper's n = 1e10 cm^-3, T_e = 1e4 K (deep-read computation, [memory, high] for the theory). (D) Energy-transfer factors and beam resonance (pp.5-6). Three factors not yet considered: (1) the oscillating electrons may move as a body, e.g. the beam, with lower frequency because of lower density (n_b = 3.8e6 cm^-3 from 3.1e-4 A/cm^2 at 5.1e8 cm/s gives 1.8e7 Hz); (2) the field of any unsymmetrical oscillation is unlimited in extent and 'may be primarily responsible for the detection of the plasma oscillations'; (3) a local oscillation traversed by fast electrons of fairly uniform speed excites neighbouring plasma. Resonance idea: beam waves striking the 'comparatively stationary ultimates' (the slow plasma electrons) at their natural frequency 'may coincide with the higher natural period of the latter and give rise to resonance'; streaming electrons of either kind 'withdraw energy' from the other kind's oscillation. A deep-read comparison with the later beam-plasma (two-stream) instability is [memory, medium] and is not a verdict. (E) Fig. 10 digitised at 300-600 dpi (deep read pp.13-15). Axes: wavelength in air 10-100 cm and relative ionization 1-6, both logarithmic. The 15 points span relative ionization 1.19-4.09 (factor 3.4, 0.54 decade) and wavelength 26.4-81.4 cm (370-1140 MHz). Least-squares log-log slope -0.60 +/- 0.16 (15 points) and -0.61 +/- 0.09 (13 points without the outliers). Slope 0 rejected (p = 0.003), slope -1 rejected at p = 0.03 (all) and 0.001 (13 points), slope -1/2 consistent (p = 0.56 and 0.23). The line drawn on the figure is labelled 'SLOPE = -0.5' but measures -0.67 on its own axes. The authors say the error is in the ionization values ('too much reliance is not to be placed on them'); with error in x a y-on-x fit is biased toward 0 and the reverse regression gives -1.16, so the data exclude 0 but cannot sharply separate -1/2 from -1. Outliers: #4 (rel. ion. 1.47, 81.4 cm) and #5 (1.47, 27.8 cm), at the same ionization but frequencies differing by a factor 2.9. Point 5 (1079 MHz) matches the quoted low-scattering 1080 MHz, and points 3 and 9 (659 MHz) match the high-scattering 660 MHz; this link is the deep reader's inference, the paper does not say which points come from which run. (F) Figs. 8-9 (p.14). Collector currents at 20 mA emission, 27 V anode: high scattering about 333 uA at +10 V and 503 uA at +20 V, low scattering about 161 uA and 380 uA (ratio about 2.1 at +10 V); ion currents at large negative collector voltage about -55 to -75 uA in both states (authors: ions 'preponderating by about 3 percent' in the low-scattering state). Switch-over at about 22 V collector; the text says high to low on raising the voltage, but the arrow in Fig. 8 points from the low curve toward the high one (unresolved, possibly a drafting slip). Emission ranges in Fig. 9: low scattering only at 10 and 15 mA, both states at 20 and 25 mA, high scattering only at 35 mA. Hysteresis: anode set to 27 V from a high value gives the high-scattering state, from a low value the low state; a bar magnet switches the state. (G) Other experimental details [read: pp.11-16]: below 19.5 C the 115 MHz peak dropped sharply and its frequency jumped to about 900 MHz; a magnetic field turned the 115 MHz wave into a 730 MHz wave; 60-75 V anode is where oscillations and scattering both disappeared (first tube, 10 mA, 0.0125 cm filament, 2 mH coil; page-label ambiguity noted by QE, the quote is on PDF p.13). The authors call the runs meant to elucidate the scattering correlation 'inadequate'. (H) People and record. Printed on p.16: 'Research Laboratory, General Electric Company, Schenectady, N.Y., November 20, 1928' [read: p.16]. Acknowledgements: Sir J. J. Thomson (suggested by letter the div-E method of p.4), H. M. Mott-Smith Jr. (help with the theory; unpublished infinite-plane-train theory cited on p.15), S. Sweetser (help with the experiments) [read: pp.4, 15, 16]. The paper cites J. S. Webb and L. A. Pardue, Phys. Rev. 31, 1122 (1928) and 32, 946 (1928) [read: page image p.8]; the second is titled 'Ionic Oscillations in the Glow Discharge' (DOI 10.1103/physrev.32.946) [web] https://api.crossref.org/works?query.bibliographic=Pardue+Webb+1928 . Earlier, independent experimental work on the ion branch, which Tonks and Langmuir compared with their sound-wave range on p.8. The 1939 replication authors are Harrison J. Merrill and Harold W. Webb [web] https://api.crossref.org/works/10.1103/PhysRev.55.1191 ; the 1928 author is printed J. S. Webb, so the two are not shown to be the same person (different initials; not proof either way).

Key claims

• A uniformly neutral ionized gas has a natural electron oscillation frequency nu_e = (n e^2/(pi m))^(1/2) = 8980 n^(1/2) cycles/s (Gaussian units), independent of the geometry of the displacement.
• Plasma-electron oscillations have zero group velocity in the model used (no space derivatives in eqs. 5B, 5C), so they show phase patterns but do not carry energy through the plasma.
• Electromagnetic waves in an electron plasma obey nu^2 = n e^2/(pi m) + c^2/lambda^2, so the plasma frequency is the low-frequency limit for long waves.
• With Boltzmann electrons, ion oscillations follow nu^2 = (n e^2/(pi m_p))/(1 + n e^2 lambda^2/(pi k T_e)), tending to the ion plasma frequency for short wavelengths and to sound-like waves with v = (k T_e/m_p)^(1/2) for long wavelengths, with the changeover within about a ten-fold change of wavelength.
• In a mercury arc with n = 1e10 cm^-3, plasma-electron oscillations are expected at about 9e8 Hz (33 cm) and plasma-ion oscillations at 1.5 MHz and below.
• Charge separation in a plasma is strongly resisted: displacing the electrons by one spacing (4.6e-4 cm at n = 1e10) gives about 8.3 V/cm.
• Hg-arc discharges produce radio-frequency oscillations of 1e7 to 1e9 Hz, detected with a crystal detector, and a critical oscillation near 231-263 MHz exists only within about 19-21 C of mercury-appendix temperature.
• Observed wavelengths in the 300+ MHz range vary with relative ionization with the -1/2 slope predicted by eq. (6) (the authors: 13 of 15 observations within the accuracy of the ionization measurement; digitised Fig. 10 gives a log-log slope of -0.60 +/- 0.16, consistent with -1/2, inconsistent with 0, with the data unable to sharply separate -1/2 from -1 given error in the ionization axis).
• The arc can sit in two stable states (high or low electron scattering) with oscillation frequencies of 660 MHz (high scattering, 28 V anode) and 1080 MHz (low scattering, 26 V anode), a ratio of 1.64 that the authors call 'almost twice', switchable by a magnet or by the voltage history.
• A resonance at 1.38 MHz near the predicted ion limit of 1.5 MHz was located by a tuned circuit, but a tuned amplifier showed a continuous spectrum (the authors say this was not confirmed).
• The authors suggest that such oscillations may account for the anomalous electron scattering and energy gain (primary electrons exceeding the tube voltage) seen in low-pressure Hg arcs (stated as a suspicion).
• The 300+ MHz oscillation frequency and amplitude are independent of collector potential from -80 V with respect to the cathode to 5 V above anode potential, and are unchanged by reversing the filament heating current (p.13).
• The authors state that the oscillation voltage amplitudes 'appear to be very small' (crystal readings of about 9 mV to about 90 mV) yet 'play a fundamental role in high current gaseous discharges' (p.2).
• The abstract suggests 50-60 MHz may be beam-electron oscillations, but the body (p.16) says the 55 MHz line cannot be identified with the computed 18 MHz beam oscillation.
• Fast thermal electrons drop out of the effective density, so frequency should fall with decreasing wavelength and oscillations below a minimum size may be impossible (p.6; the authors give no calculation; the sign is opposite to later Bohm-Gross dispersion).
• Oscillating beam waves may strike the slow plasma electrons at their natural frequency and give rise to resonance (p.6).

Relevance: This is the only document and the origin of the plasma-oscillation concept. It introduces the term 'plasma' for the quasi-neutral region of a discharge and derives the plasma frequency and the ion-acoustic dispersion relation. The project is mainly a history and learning project: the theory matches textbook results, while the experimental part is an early and incompletely resolved attempt to link the oscillations to the scattering anomaly.

Mainstream conflict: None in the theory. Plasma frequency, the dispersion relation and ion-acoustic waves are standard plasma physics. The experimental attribution of the electron-scattering anomaly to these oscillations was a 1929 hypothesis and is not settled by this document; the paper itself reports that the beam-oscillation fit and the tuned-amplifier check did not confirm cleanly. Mainstream status of the later explanation is not read from the documents. One specific conflict inside the theory: the p.6 qualitative thermal argument predicts frequency decreasing with decreasing wavelength, whereas Bohm-Gross dispersion (1949) has it increasing [memory, high; deep read pp.5-6]. The abstract's beam-oscillation reading of 50-60 MHz is withdrawn in the body (p.16).