sharma_2018

A. Sharma, M. N. Slipchenko, M. N. Shneider, X. Wang, K. A. Rahman and A. Shashurin, “Counting the electrons in a multiphoton ionization by elastic scattering of microwaves”, Sci. Rep. 8, 2874 (2018)

Source record · Catalogue · Review register

DOI: 10.1038/s41598-018-21234-y

Source kind: measurement

Recorded technique: Absolute electron counting by Rayleigh microwave scattering (RMS; pp. 2-4, 8-9): a 10.8 GHz homodyne system (I/Q mixer, horns 6 cm from the plasma, response time about 250 ps), the microwave field linearly polarised along the plasma channel; the scattered field of the thin channel is that of a Hertz dipole, U_out ~ E_s = e^2 omega E_i N_e / (m c^2 nu r) (Eqs. 5-7), and the system is calibrated absolutely with Teflon ‘bullets’ (3.175 mm diameter, 1 cm long) shot through the field, giving A = 2.12 x 10^5 V Ohm m^-2 and ‘N_e = U_out x 4.81 x 10^13’ (pp. 8-9, Fig. 6). Plasma: air (relative humidity 30 %, about 300 K) ionised by an 800 nm Ti:sapphire laser, 100 Hz (lowered from 1 kHz so that the electron number no longer depended on the repetition rate), focused by a 1000 mm plano-convex lens (7 mm beam on the lens), the energy set by a linear polariser and measured with a power meter (Gentec-EO XLP12-3S-H2-DO). Beam: the 1/e^2 radius from beam-profiler images of the attenuated beam along z (Fig. 2(a,b): R_x = 92.17 um, R_y = 94.41 um at the waist, w = (R_x R_y)^1/2 fitted with w0 = 93.28 um, z_R = 26.98 mm, ‘M^2 = 1.3’); the duration from an SHG intensity autocorrelation, ‘nearly Gaussian shape with full width at half maximum (FWHM) equal to 232 fs’, so a Gaussian pulse of FWHM 232 / 2^1/2 = 164 fs (p. 4). Table 1 (p. 5): the means of repeated measurements with their standard errors. The O2 eight-photon cross section follows from fitting N_e = (231 pi / (1024 x 16)) (pi / 8)^1/2 sigma_8 n0 tau pi w0^2 z_R I0^8 (Eq. 4) to the measured N_e(I0) below 2.7 x 10^13 W/cm2, with n0 ~ 5.13 x 10^18 cm^-3 the O2 density of the air (p. 6).

Materials in structured entries: O2

Dataset quantities: multiphoton_ionization_cross_section

Contents: 1 dataset; 0 formulas.

Curation notes

Sci. Rep. 8, 2874 (2018), 10 pp.; PDF pages 1-10 = article pages 1-10. Identity checked on PDF p. 1 on 2026-10-01: ‘Counting the electrons in a multiphoton ionization by elastic scattering of microwaves’, A. Sharma, M. N. Slipchenko, M. N. Shneider, X. Wang, K. A. Rahman and A. Shashurin (Purdue, Princeton); ‘Scientific REPOrTS | (2018) 8:2874 | DOI:10.1038/s41598-018-21234-y’; received 10 November 2017, accepted 31 January 2018. Open access (CC BY 4.0).

THE VALUE. ‘the MPI cross-section was determined to be sigma_8 = (3.3 +- 0.3) x 10^-130 W^-8 m^16 s^-1’ (p. 6; also the abstract and p. 7), defined by the ionisation rate nu = sigma_8 I^8 per O2 molecule, I the local instantaneous intensity (p. 2); ‘eight-photon’ because ‘E_i = 12.2 eV and ... hbar omega = 1.55 eV’ (p. 3). In other units (computed, not printed): 3.3 x 10^-98 s^-1 (cm2/W)^8, i.e. nu = 9.3 x 10^9 s^-1 at 2.7 x 10^13 W/cm2.

WHAT +-0.3 IS. Not defined. It is stated after the fit of ‘this initial segment of the dependence’ (p. 6) and is smaller than what the pulse duration’s uncertainty alone carries (below), so it reads as the fit’s uncertainty only. Taken here as the dataset’s sigma, level ‘not stated’, with the systematic part below in the notes, not in the number.

WHAT IT RESTS ON. (a) The pulse: the intensity profile is taken Gaussian in time, I ~ exp(-t^2 / tau^2), with tau = FWHM / (2 (ln 2)^1/2) = 98.6 fs (p. 4) from the 164 fs FWHM, itself 232 fs / 2^1/2 from an autocorrelation ‘nearly Gaussian’ (the shape is assumed, not measured; 164 / (2 (ln 2)^1/2) = 98.5 fs, the Table’s 98.6 +- 5.2 fs being a mean of measurements). So tau is the 1/e half-width of the intensity, not a FWHM. (b) How I0 was obtained is not printed; ‘All parameters of the beam in Equation (3), namely I0, w0, z_R, and tau, are determined experimentally’ (p. 3), the energy with a power meter. If I0 = 2E / (pi^3/2 w0^2 tau), as for this Gaussian beam, Eq. 4 gives sigma_8 ~ N_e tau^7 w0^14 / (z_R E^8): the duration’s 5.3 % (5.2 / 98.6, Table 1) is about 37 % in sigma_8 (7 x 5.3 %), the waist’s 0.75 % about 10 %, z_R’s 1.1 % 1 %, and the energy’s calibration (not stated) enters to the eighth power. (c) The electron number: the scattered signal is ~ N_e / nu (Eq. 7), so N_e and sigma_8 scale with the assumed electron-gas collision frequency: ‘We used nu_eg = 5.18 x 10^11 s^-1 based on electron-gas elastic collision cross-section sigma_eg = 5 x 10^-16 cm^-2 [sic, cm^2] and electron temperature T_e = 0.4 eV’ (p. 8), neither measured; Eq. 9 as printed drops the nu (A x e^2 / m x N_e for the plasma), which the calibration constant cannot absorb since A is fixed with the dielectric. tools/extract/sharma_2018.py reproduces nu_eg = N sigma_eg v_mean with N the air density at 1 atm and 300 K and v_mean = (8 k T_e / pi m_e)^1/2 (5.18 x 10^11 s^-1), and n0 as 20.95 % of N (the O2 fraction of dry air, not printed). (d) The range: ‘N was fitted by the I0^8-law for intensities I0 < 2.7 x 10^13 W/cm2’ (p. 6), where the focal plane did not shift (Kerr and plasma effects negligible for I0 <= 2.68 x 10^13 W/cm2, p. 4, Fig. 2(f)); ‘Deviation from the I0^8-law for higher intensities ... can be explained by relative proximity of Keldysh parameter gamma to 1 ... and action of Kerr nonlinearity’ (p. 6). The lower end of the fitted range is not printed (Fig. 3(b), an image, not read: the printed sigma_8 is the result, data rule 8).

COMPARISONS printed (not checked here): the semi-empirical rates of Talebpour et al. (ref. 20) ‘underestimated the photoionization rates about 2-3 times, while purely theoretical predictions in ref. 24 seem to slightly overestimate the rates’ (p. 6, Fig. 3(c)); the introduction quotes Talebpour’s ‘3 x 10^9 s^-1 for O2 for the laser intensity 3 x 10^13 W/cm2’ (p. 2), where sigma_8 I^8 gives 2.2 x 10^10 s^-1 (a factor 7; 3 x 10^13 is above the fitted range).

The beam parameters are Table 1’s (library table tbl_99fbcc35e0aa), checked against it by tools/extract/sharma_2018.py, which writes no data file.

Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets

sharma_2018/sigma8_O2

{
  "id": "sigma8_O2",
  "material": "O2",
  "table": "text",
  "scale": 1e-130,
  "quantity": "multiphoton_ionization_cross_section",
  "unit": "W-8 m16 s-1",
  "abscissa_unit": "nm",
  "use": "check",
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "photons": 8,
    "wavelength_nm": 800,
    "pulse_fs": 164,
    "pulse_fs_definition": "FWHM of the intensity, 232 fs / 2^1/2 from an SHG intensity autocorrelation taken as Gaussian",
    "tau_fs": 98.6,
    "tau_fs_sigma": 5.2,
    "tau_definition": "I ~ exp(-t^2 / tau^2): the 1/e half-width of the intensity, FWHM / (2 (ln 2)^1/2); Table 1, mean +- standard error",
    "waist_um": 93.3,
    "waist_um_sigma": 0.7,
    "waist_definition": "1/e^2 radius of the intensity at the focus (Table 1, mean +- standard error); w = (R_x R_y)^1/2, R_x = 92.17, R_y = 94.41 um",
    "rayleigh_length_mm": 26.9,
    "rayleigh_length_mm_sigma": 0.3,
    "m2": 1.3,
    "o2_density_cm3": 5.13e+18,
    "collision_frequency_s": 518000000000.0,
    "collision_frequency_basis": "assumed: sigma_eg = 5e-16 cm2 (printed 'cm^-2'), T_e = 0.4 eV",
    "intensity_range_W_cm2": "below 2.7e13 (the fit; lower end not printed)",
    "medium": "air, relative humidity 30 %, about 300 K; sigma_8 is O2's (the O2 rate 2-3 orders above N2's, p. 3)",
    "polarization": "linear",
    "polarization_note": "the laser's state is not stated in words; the pulse energy is 'varied using a linear polarizer' (p. 3)"
  }
}

1 inline points in the source record.

p. 6 (and the abstract, p. 1; the conclusion, p. 7): ‘sigma_8 = (3.3 +- 0.3) x 10^-130 W^-8 m^16 s^-1’, the eight-photon ionisation cross section of O2 at 800 nm, nu = sigma_8 I^8 per molecule, from absolute electron numbers (microwave scattering) in air fitted below 2.7e13 W/cm2. Printed as 3.3 and 0.3 with the scale 1e-130. The +-0.3 is not defined and reads as the fit’s alone (the record’s notes): the pulse duration’s 5.3 % carries about 37 % (sigma_8 ~ tau^7 at fixed energy), the waist’s 0.75 % about 10 %, and the electron number scales with the assumed collision frequency nu_eg = 5.18e11 s^-1. In s^-1 (cm2/W)^8: 3.3e-98 (computed).

Formulas

No formulas are recorded.

Corrections

No dataset errata are recorded in this source record.

Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.