Numerical Simulation of Electron Amplification Process in MicroChannel Plate by Using Furman's Model
Hideki Kawaguchi*, and Yoshihiro Ito*** Division of Information and Electronic Engineering, Graduate School of Engineering,
Muroran Institute of Technology, Japan** Department of Information Science and Technology,
Yuge National College for Maritime Technology, Japan
Abstract— In measurement devices of very high-speed phenomena such as the framing camera and streak camera, theMicro Channel Plate (MCP) plays very important role for amplification of very small signals. It is necessary to understandthe electron amplification process of the MCP for further improvement of these high-speed mesurement devices. Thispaper presents a numerical simulation method of the MCP based on the Monte Carlo calculation and Furman’s secondary
electron emission model. It is shown that electron amplification phenomena by the secondary emission in the MCP can besimulated.
Keywords— Micro Channel Plate (MCP), FDM, Monte Carlo Method, Furman's model, Lorentz equation of motion,
Runge-Kutta method, Electrostatic field.
1. Introduction
For measurements of ultra high-speed phenomena of orderof several hundred pico-second accompanying with lightemission as in plasma processing, luminous phenomenon ofsemiconductor, beam physics, etc., the framing camera andstreak camera have been frequently employed. One of core
parts of such the high speed measurement devices is the Micro
Channel Plate (MCP). In general, the light signals in such highspeed phenomena are very weak intensity and it is necessary tobe amplified for effective measurement. But the light signal
itself can not be amplified directly. Then the MCP has
important role of signal amplification in such high speedmeasurement devices. In the MCP, the light signal is once
converted to electron beam density distribution and after that thesignal is amplified as the form of electron beam by using thesecondary electron emission phenomena. Accordingly in thecase of ultra-high speed phenomena of order of several picosecond, linearity of amplification of signals may be lost in thesecondary electron emission process.
Then quantitative
understanding of amplifying mechanism of the electron beam in
the MCP is essential for design and development of such theultra high speed measurement devices. To aim to analyze thecascading emission process in electron amplifier operation ofthe MCP, we present the Monte Carlo simulation code by using
Furman’s secondary electron emission model [1].

2. MCP in framing camera
As an example of signal amplifications in the MCP, an overview
of the framing camera system is shown in Fig.1. The light signal
is assumed to come from upper direction. The incoming light isconverted to electron beam density distribution depending on
the original signal intensity at the photo cathode. The generated
electrons at the photo cathode are accelerated toward to theMCP. The MCP is composed of dielectric material plate withover million inclined channels of about 10 μm diameter (Fig.2).
When the electrons arrive at the MCP, most of electron getenter to the micro channels and hits to the inclined channel wall.
As a result of this event, the secondary electrons are emitted at

Micro channel

Fig. 2 Micro channel plateElectrons

Light image signal

Micro channel

Electrons
Photo cathode

MCP

Phosphor

Amplified light signal

Fig. 1 Overview of framing camera system

Fig. 3 Electron beam amplification in micro channel

this hitting point on the wall. The emitted electrons areaccelerated by imposed voltage between top and down surfaceof the MCP, and the secondary electron emission will repeats
many times during all the electrons pass though the channel(Fig.3). The amplified electron beam is extracted from the otherside of the MCP, and re-converted to the light signal on thephosphor. And finally the amplified light signal will becaptured by the CCD camera. Then, inverse DC bias is applied
ordinarily to the MCP to avoid passing of unnecessary signals.
When measurement signal arrives on the MCP input surface, theshuttering pulse will be applied to the MCP electrodesynchronizing with the incoming signal and begin the amplifierprocess in the MCP channel.
3. Simulation of electron amplification process
We here assume that the measurement signal is of order ofnanosecond. This time range corresponds to several meters
wavelength which is much larger than the thickness of the MCP,
of order of 100 micrometers. Accordingly the electric field E(x)can be regarded as static and there is no magnetic field. In
addition, the number of electrons inside the MCP channel is at
most several millions. This means that space charge effects
caused by electrons are much smaller than the electric field
produced by applied voltage on the MCP. In this case, theelectric field is simply described by Laplace's equation,(1)
 ( (x))  0, E( x)   ( x)On the other hand, the charged particle equation of motion
under the static electric field is as follows,. dp(t )  eE( x(t )), p(t ) dt

mv (t )
 v(t ) 1  c (2)2The particle velocity easily reaches to relativistic region due tosmall electron mass, therefore the relativistic effects have to beincluded in the particle simulation.
The most complicated part of the MCP simulation is appropriate
description of the secondary electron emission on the MCP
channel surface. We here adopt Furman’s secondary electronemission model which was developed for simulation of electron
cloud effects in particle accelerator science [1]. In Furman'smodel, three kinds of secondary electron emissions for theincident electron beam current I0 are assumed, the backscatteredelastic electron beam current Ie, the rediffused electron beam
current Ir and the true-secondary electron beam current Its(Fig.4). The number of the secondary emitted electrons, emitted
electron energy and momentum are calculated by using theMonte Carlo simulation depending on individual generation
probability of each currents. The biggest advantages of thismodel are treatment of more than two kinds of secondary
electron emission currents and exact conservation of electronenergy and generation probabilities. On the other hand, there
exist many fitting parameters depending on emission surface
material in Furman's model. Especially the fitting parameters
for reduced lead grass which is MCP channel surface material is
not specified yet. To develop the MCP simulation code, theFurman's fitting parameters for the MCP channel material isidentified compared with an experimental result [2] in this paper.
4. Numerical simulation
Although the actual MCP consists of about 1000 x 1000 microchannels with honeycomb arrays (Fig.2), we use here single
channel model to compare with the experimental result forsimplicity. The cross-section of uniform grid numerical modelof the single channel MCP is shown in Fig.5(a). The diameterof the micro channel is 10 μm and the length of the microchannel is 460 μm. It is assumed that inside of the channel isvacuum, and relative permittivity of the MCP material is 6.0.
Laplace's equation (1) is numerically solved by the FDM on thisgrid and the equation of motion (2) is integrated by 5th order
Runge-Kutta (R-K) method combined with Furman's model forthe secondary electron emission. Especially the rediffusedelectron beam current Ir is not included in this simulation since
this current Ir is not considered in Ref.[2]. The figure 5(b) shows
numerical example of electron amplification phenomena by
repeating the secondary emission.
5. Conclusion
For quantitative understanding of electron amplification process
in the MCP, numerical simulation code of the secondary
electron emission phenomena is developed based on the FDM
for electrostatic field and the R-K method combined with theMonte-Calso method for electron motion. For a further progress,
we will quantatively compare the numerical simulation withexperimental results of electron amplificaiton gain.
References[1] M.A.Furman, M.T.F.Pivi, “Probabilistic Model for the Simulationof Secondary Electron Emission,” SLAC-PUB-9912, pp.1-19 , 2003.
[2] M.Wu, C.A.Kruschwitz, D.V.Morgen, J.Morgen, ”Monte Calro
Simulation of Micro Channel Plate Detector I. Stady-state Voltage
Bias Results,” Rev.Sci.Instrum., Vol.79,073104, 2008.

I0Ie
I tsFig. 4 Electron currents in Furman's modelIr(a) numerical model(b) electron trajectories
Fig. 5 Numerical example of single channel model of MCP