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Multiple scattering effects on quantum efficiency and response time for cesiated metal photocathodes
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Image of FIG. 1.
FIG. 1.

(Color online) Scattering times as a function of energy for acoustic (green square), electron-electron (blue diamond), and total (red circle) for 77 K (dash) and 300 K (solid line). At 1.6 eV above the Fermi level, the e-e and acoustic relaxation times are 20.4 and 107 fs, respectively, at 300 K.

Image of FIG. 2.
FIG. 2.

(Color online) Time slices at every 6 fs (starting at 2 fs) of 1000 photoexcited electrons in bare copper for the Fatal approximation (blue top), allowing one scattering event (green middle) and allowing all scatterings (red bottom). All electrons whose energy falls below the surface barrier are removed from visualization. Red electrons move toward the surface (to the right) and blue electrons move away (to the left). The images are similar, implying the Fatal approximation is reasonable. Length of simulation region is approximately 12 nm.

Image of FIG. 3.
FIG. 3.

(Color online) Same as Fig. 2, but for Cs–Cu. The time slices are every 8 fs starting at 4 fs. The figures are different, implying that scattered electrons may nevertheless still be emitted if conditions are favorable. Length of simulation region is approximately 16 nm.

Image of FIG. 4.
FIG. 4.

(Color online) Evolution in mean energy of electrons for which and a standard deviation σ for Cu parameters. After two scatterings, less than 1% of the initial 106 electrons remain.

Image of FIG. 5.
FIG. 5.

(Color online) Same as Fig. 4 but for Cs–Cu parameters. After eight scattering events, less than 1% of the initial 106 electrons in the simulation remain, but assigning a % loss factor after each scattering is impractical because the mean energy changes and therefore also changes.

Image of FIG. 6.
FIG. 6.

(Color online) The emitted electrons as a percentage of the initial number for Cu parameters (blue square) or Cs–Cu (red circle). Primary (solid symbols and lines) indicates photoexcited electrons; secondary (open symbols and dashed lines) indicates electrons excited by collisions with the photoexcited electrons.

Image of FIG. 7.
FIG. 7.

(Color online) The ratio of the number of emitted secondaries to number of emitted primaries for the Cs–Cu data of Fig. 6 as a function of photon energy, and compared to Eq. (5).

Image of FIG. 8.
FIG. 8.

(Color online) Emitted electrons are from two population types: the left are modeled as an expanding spherical shell of charge; the right are modeled as a diffusively expanding sphere with a Gaussian distribution of charge. The origin of each (circle) is within the copper (grey) surface.

Image of FIG. 9.
FIG. 9.

(Color online) Emitted charge as a function of time for bare copper parameters (266 nm photons, 4.5 eV work function, 10 MV/m field). The inset equation is Eq. (6). The initial number of electrons is 106.

Image of FIG. 10.
FIG. 10.

(Color online) Same as Fig. 9, but for cesiated copper parameters (266 nm photons, 1.6 eV work function, 10 MV/m field). Using Eqs. (6) and (7) with the parameters Qs = 14 828, Qd = 69 127, and τ* = 2.53 fs gives the best least squares correspondence (t0 is fixed at 3.42 fs).

Image of FIG. 11.
FIG. 11.

(Color online) Same as Fig. 10, but on linear axes to show long time behavior.

Image of FIG. 12.
FIG. 12.

(Color online) Current as obtained from the time derivative of Eqs. (6) and (7) using parameters extrapolated from Fig. 11.

Image of FIG. 13.
FIG. 13.

(Color online) Histograms of energy distribution of emitted electrons from copper: (left) total energy; (middle) transverse energy; (right) normal energy. Legend is labeled by number of scattering events plus one: n = 1 (no scattering) is the fatal approximation; n = 2 is fatal + one scattering event, as considered by Berglund and Spicer in Ref. 8 For copper further changes beyond n = 3 are not perceptible.

Image of FIG. 14.
FIG. 14.

(Color online) Same as Fig. 13 but for cesium on copper. The energy distribution is much more broad due to the small work function, and scattering up to n = 10 give visible changes.

Image of FIG. 15.
FIG. 15.

(Color online) Percentage of emitted electrons as a function of number of tangible scattering events they had. For copper (blue square), less than 1% of the total number of electrons have had more than one scattering; for cesium on copper (red dot), roughly half of the emitted electrons have experienced one or more scatterings before emission.

Image of FIG. 16.
FIG. 16.

(Color online) Emitted charge (black squares) is the sum of two populations: those electrons that do not scatter before emission (red circles) and those that do (blue diamonds). When , the contribution of scattered electrons is small, i.e., the Fatal approximation is good. When , the two populations are comparable. Each simulation began with 105 electrons.

Image of FIG. 17.
FIG. 17.

(Color online) Using Monte Carlo, the ratio of the total emitted charge with the unscattered charge, anticipated to be proportional to the ratio of the full QE with the QE calculated using the Fatal approximation. Variations in wavelength for a given work function are black solid and open circles. Variations in work function for a given wavelength for cesium on copper (Cs–Cu) parameters are colored diamond, square, and triangle symbols. An analytical fit to the shorter wavelength Cs–Cu conditions is also shown.

Image of FIG. 18.
FIG. 18.

(Color online) Comparison of the moments-based predictions of QE from bare copper using the nonfatal approximation (red solid line) and the fatal approximation (blue dashed line) with data from Fig. 8 of Ref. 21 (data courtesy of D. Dowell).

Image of FIG. 19.
FIG. 19.

(Color online) Work function of submonolayer coatings of cesium on copper (dashed lines) and tungsten (solid lines) for various f (labeled by crystal face) using Gyftopoulos–Levine theory. Experimental measurements herein correspond to the [B] line.

Image of FIG. 20.
FIG. 20.

(Color online) Images of the surface of a sintered tungsten dispenser cathode surface. Different crystal faces have different gray scales associated with them.

Image of FIG. 21.
FIG. 21.

(Color online) Same as Fig. 17, but R(x) for cesium on tungsten (Cs–W) parameters. The coefficients and power differ, and there is some variation with wavelength, but a useful analytical fit is shown.

Image of FIG. 22.
FIG. 22.

(Color online) Comparison of the QE obtained by experiment at UMD for various wavelengths (shown on left-hand-side in the same color and relative height as the peak QE). Theory was calibrated by relative peak location and height of the green data line. It is seen that the R(x) prefactor better accounts for both shape and comparative magnitudes of the different QE relations.

Image of FIG. 23.
FIG. 23.

(Color online) The normalized current functions B(x,n) and D(x) for unscattered and diffusive emission. “Shell” refers to the B function with the number following “shell” indicating the value of n. The dashed line corresponds to the diffusive emission term of Eq. (11).


Generic image for table
Table I.

Parameter values and units and definitions and representative values of parameters used in calculations.

Generic image for table
Table II.

Copper, tungsten, and cesiated values. Terms used in the evaluation the relaxation times for copper, cesiated copper, tungsten, and cesiated tungsten in both Monte Carlo and moments QE numerical evaluations (adapted from Refs. 29, 38 except for μ(W) which is taken from Ref. 76).


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Multiple scattering effects on quantum efficiency and response time for cesiated metal photocathodes