Microchannel Plate
MCP gain, spatial resolution, and effective QE for photon detectors.
L/d Ratio α
50.0
10.0 wall strikes, δ = 2.000 per strike
Single-Plate Gain
1.02e+3
(A·V/(2α√V₀))^(4V₀α²/V)
Total Gain, 2 Plates
1.05e+6
Unsaturated product, above the one-channel space-charge limit
Space-Charge Limit (one channel)
1.00e+6
10⁸ × d / 1 mm
Optimum L/d at This Voltage
60.7
Peak single-plate gain 1.57e+3
Channel Pitch (hexagonal)
12.29 µm
Sets the resolution of a single plate
Detection Efficiency
15.0 %
QE × open area (electrons that miss a channel are lost)
Pulse-Height Distribution
Quasi-Gaussian
Stack product above the one-channel limit: the rear plate begins to saturate. Charge spreads over several rear channels, so Wiza reports (1–4)×10⁷ peak gain and 60–170 % FWHM for chevrons
Key Formulas
α = L/d; wall strikes n = 4V₀α²/V; yield per strike δ = A·√V_c = A·V/(2α√V₀)
Gplate = δn = (A·V/(2α√V₀))^(4V₀α²/V)
αopt = A·V/(2√(e·V₀)), Gmax = exp(A²V/(2e))
Gsat ≈ 10⁸ × d/1 mm (space charge at the channel output)
Pitch p = d·√(π/(2√3·OAR)); η = QE × OAR
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Schagen's model: secondaries leave the wall normally at V₀ and yield A·√V_c per strike. With A = 0.2 a 1 kV plate of L/d 50 gives 10³ where real plates give about 10⁴, so fit A to a measured curve. Stacks multiply unsaturated against the one-channel space-charge limit; chevrons saturate near 10⁷. Saturation is flagged against the one-channel limit. No ion feedback.
- Wiza J. L. (1979). Microchannel plate detectors. Nucl. Instrum. Methods 162, 587–601, eq. (1)–(4) and §2.2. Schagen's channel-gain model (eq. 1) with A ≈ 0.2 and V₀ ≈ 1 eV, exponential pulse heights below saturation, saturated gain proportional to the channel diameter (10⁸ for 1 mm). doi:10.1016/0029-554X(79)90734-1