Download Zahn, M., M. Hikita, K.A. Wright, C.M. Cooke, and J. Brennan, Kerr Electro-optic Field Mapping Measurements in Electron Beam Irradiated Polymethylmethacrylate, IEEE Transactions on Electrical Insulation EI-22, pp. 181-185, April 1987

IEEE Transactions on Electrical Insulation Vol.. EI-22
No.2. April 1987
1lei
KERR ELECTRO-OPTIC FIELD MAPPING MEASUREMENTS
IN ELECTRON BEAM IRRADIATED POLYMETHYLMETHACRYLATE
M. Zahn, M. Hikita*, K. A. Wright, C. M. Cooke and J. Brennan
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
Laboratory for Electromagnetic and Electronic Systems
High Voltage Research Laboratory
Cambridge, MA
ABSTRACT
Kerr electro-optic field mapping measurements are presented
in electron beam irradiated polymethylmethacrylate (PMMA) where
the accumulated trapped charge results in large self-electric
fields of the order of 1 to 2.5 MV/cm. The resulting numerous
light maximum and minimum recorded on photographic film and
videotape allow accurate measurement of the time dependence of
the electric field and space charge distributions.
I NTRODUCTION
Recent Kerr electro-optic field mapping measurements
in polymethylmethacrylate (PMMA) had a maximum applied
electric field of the order of 3.5x105 V/cm [1,2]. The
measurement required the use of a photomultiplier tube
as a light detector because of the small Kerr constant
of PMMA. Our work uses an electron beam to irradiate
PMMA samples where the accumulated trapped charge leads
to higher internal self-electric fields [3,4] so that
for a 10 cm long PMMA sample, numerous light minimum
and maximum arise, making photographic and videotape
measurements possible.
The motivation for this work is in part due to understanding electron-caused discharges along insulating
surfaces on spacecraft. It is hoped that Kerr electrooptic field mapping measurements will allow the development and verification of models leading to a better understanding of radiation effects on solids.
EXPERIMENTAL METHOD
The linear polariscope configuration in Fig. 1 has
incident light in the z-direction polarized at +450 to
the direction of the electric field E with an analyzing
polarizer placed after the sample either crossed or
aligned to the incident polarization. The He-Ne laser
at 633 nm wavelength has its beam expanded to t7.5 cm
to allow measurements of the light intensity distribution over the entire sample cross section. Beam split-
ters allow simultaneous measurements for aligned and
crossed polarizers using Polaroid® cameras as well as a
videotape recording system. The resulting transmitted
light intensity as a function of (x,y) position over the
sample cross section is then:
sin
I(x,J)
Im
2f
iE(E,]
[
+
1m(XYII
Crossed
Polarizers
(x Y)j
Aligned
Polarizers
(AP)
-
cos2}W
E
(CP)
(1)
where 6m(x,y) is the initial field independent mechanical birefringence phase shift before irradiation, Im is
the maximum light intensity and
EmEm
1
B-
(2)
where B is the Kerr constant of PMMA and L is the sample length in the direction of light propagation.
Fig. 2 shows representative photomultiplier tube
(PMT) responses with aligned and crossed polarizers
with He-Ne laser light at 633 nm wavelength for a sample L=1.09 m long and d=0.635 cm thick between parallelplane electrodes stressed by a high-voltage pulse v(t).
With no electric field (E=0) separate measurements with
aligned and crossed polarizers allowed determination of
Tm and 6m. Early in the pulse v(t), space charge effects are negligible and the electric field in the central region is uniform at E=-v(t)/d. With crossed and
aligned polarizers we then measured the voltage Vm required for the first light maximum (crossed polarizers)
or minimum (aligned polarizers) so that the total phase
6 for either aligned or crossed polarizers for the
trigonometric functions in (1) is Tr/2. For this long
sample we found Vm to be z96. 5 to 99 kV so that
Em-'Vm/d'152 to 156 kV/cm. From (2) we then obtained
B-2X10-15 m/V2, in agreement with a previously published
0018-9367/87/0400-0181$01.00 CD 1987 IEEE
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IEEE Transactions on Electrical Insulation Vol. EI-22 No.2, April
182
ERIZED
GE
ZER
1987
Electron Beam Energy 2.6 MeV
Current Density 120 nA/cm2
Time II seconds
(Ern0.44 MVI/cm)
Aligned Polarizrrs
Before Irrodiohon
R_
LENS
Aligned Polarizers
Crossed Polarizers
BEAM
EXPANDER
Bctor. Irrodiftion
EMgyy 26 uV
Current Dmnsity 20 nA/cm2
Tim 60 seconds
Electm, Sbe
(Em-05 MV/cm)
TO VIDEO
SPLITTER
From Curreni Monitor A
Fig. 1: Apparatus and representative data for Kerr electro-optic field mapping measurements with simultaneous
aligned and crossed polarizers in electron beam irradiated samples using photographic film and a computer
interfaced videotape recording system as detectors.
Pro
Ground
--O
PV Croond-
PMT
115kV
-
-
HVCround
105kV
-
Fig. 2: Photomultiplier tube (PMT) outputs for 633
nm He-Ne light with negative high volZtage pulses
applZied to a PMMA sample 1.09 m Zong and 0.635 cm
thick with aligned and crossed polarizers.
value [1,2]. Note in Fig. 2 that the PMT ground is at
the top of the oscilloscope picture and that increasing
light gives a more negative signal. The high voltage
has negative polarity. In these pictures
is small
so that before voltage is applied the PMT response is
zero for crossed polarizers and maximum for aligned
polarizers. Since the peak voltage amplitude exceeds
Vm, with aligned polarizers the PMT response goes
through minimum and starts to increase to the next maximum before the collapsing voltage again reaches Vm, returning the PMT output to a broad zero before returning
to maximum as the applied voltage goes to zero. With
crossed polarizers, the PMT output is zero before voltage is applied rising briefly past the first maximum
towards a minimum as v(t)>Vm and then quickly returning
to a broad maximum as the collapsing voltage passes
through Vm again towards zero. Once we have determined
that B-2x10m/V2, we find Em for our shorter electron
beam irradiated samples to be Em0.5 MV/cm for L=10.2 cm
and EmvO.44 MV/cm for L=12.7 cm.
5m
I
The electron beam is generated by a Van de Graaff
generator and exits from the accelerator tube through
a thin (76 pm) aluminum window and passes through z50
cm air to the PMMA sample which is short-circuited
through current monitors at the top and bottom surfaces.
The energy loss in the window and intervening air is
about 160 keV. Fig. 1 shows representative data for an
accelerator beam energy of 2.6 MeV and a current density of 20 nA/cm2 after z60 s of beam irradiation for
aligned and crossed polarizers for a d"1.27 cm thick
PMMA sample uniformly irradiated over its width 5.1 cm
and length 10.2 cm. The sample had Eer0.5 MV/cm. The
sample is shown before irradiation to have some mechanical birefringence. Also shown in Fig. 1, is a representative frame of light intensity distribution of
maximum and minimum from our computerized image digitizer for a larger current density of 110 nA/cm2 after
11 s of irradiation. This sample had a length of 12.7
cm so that EmzD.44 MV/cm.
MEASUREMENTS RESULTS
Fig. 3 shows the non-uniform optical pattern on film
due to mechanical birefringence with no field and the
Kerr measurement after the short-circuited sample is
irradiated with high-energy electrons. Whereas the
peak electric field in Fig. 2 is ~160 kV/cm, the peak
field due to the trapped electrons in Fig. 3 is -1.5
MV/cm, which led to the spark discharge treeing pattern
shown.
Fig. 3 also shows how
we
manually read the photographs
distribution. We plot
to determine the electric field
the mechanical birefringence Sm(x,y=0) before irradiation which, for simplicity we take to be box-like,
either 0° or 900, neglecting the gray scale smooth
transition between maximum and minimum. We also plot
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Zahn et al.: Field mapping measurements in irradiated polymethylmethacrylate
183
n=0 bright line for a zero field with aligned polarizers. Within the sensitivity of the optical measurement,
the electric field is discontinuous across these coincident lines, so the charge is effectively a sheet of
surface charge with density |a/EEmI=2.0.
the total birefringence from the Kerr effect photograph
using the center of the dark minimum lines and the center of the light region between dark lines. To obtain
the electric birefringence, we graphically subtract.
We then calculate the electric field distribution as
plotted. Note that the short circuit imposes the constraint of zero average electric field. The electric
field is thus oppositely directed on either side of
the zero-field point.
(E/E
In the Kerr effect pattern of Fig. 3, the n=0 and
n=+1 lines have coalesced in the central region. This
obscures the n=O bright line for a zero field with
aligned polarizers. Within the sensitivity of the optical measurement, the electric field is discontinuous
across these coincident lines, so the charge at this
position is effectively a sheet of surface charge with
charge density a/CE,n=2.0.
)2
We are also using tv cameras as light detectors and
recording on videotape the field and charge build-up
when the electron beam is turned on as well as the decay when the beam is turned off. This will allow us to
determine charge trapping/detrapping parameters, charge
mobilities, and other relaxation mechanisms.
'
3
2.6MeV, 92rl/- , ]S seciond,
.'7 r-l! this:k, Al i,-:ld '.ri es
Em= ° . S MV/cm
2
E/Em
1
0
-1
-2F
-4
Fig. 3: Kerr electro-optic field mapping measurements
in electron-beam irradiated short circuited PPM, 1.27
cm thick, using aligned polarizers with cw He-Ne Zaser
light at 633 nm. Shown are the optical pattern due to
mechanical birefringence before application of the
electron beam, the resuZting Kerr effect pattern after
15 s of irradiation at energy 2.6 MeV and current density 220 nA/cm2, and the resulting treeing pattern after electrical breakdown. The data is manually reduced by the box-like approximation of mechanical birefringence 6m where a dark fringe has 6m(x)=900 and
6m(x)=o otherwise. Box-like approximation of the total
birefringence for the dark lines in the irradiated sample and the graphical subtraction to get the net eZectricaZ birefringence when E/Em=vrn, with Em-0.5 MV/cm is
shown. The resulting electric field distribution has
zero average field with peak fields at the boundaries.
Note that the zero field position in the central region
has the coalescence of n=+1 lines which obscures the
Our early measurements had tree breakdowns which
originated from the sides of the samples as in Fig. 3.
To avoid such edge effects we made oversized samples
and placed them below a lead sheet with a rectangular
cut-out smaller than the sample. The electron beam
would only pass through the cut-out and thus not irradiate the sample to the edges. Breakdowns would
then occur at higher field strengths, and would pass
through the top and bottom surfaces and not to the
sides [5]. Such was the case for the computer image in
Fig. 1 where the sample broke down after 17 s of irradiation.
A secondary problem is that the sample would gradually darken with irradiation dose from the side where
the beam enters the sample. This darkening can be seen
on the top side of the image for the computer image in
Fig. 1. This darkening becomes worse with increasing
dose and ultimately limits our optical measurements for
high doses.
Fig. 4 shows the electric field and space charge distributions as obtained from our computerized image digitization system for the images shown at various times
before electric breakdown occurred after ~6 s of 2.6
MeV electron beam irradiation at an average current
density 120 nA/cm2. Note that at time 5.76 s, the
E/Em=Yln light and dark lines with n=0 and n=+1 have
coalesced resulting in the sheet of surface charge
Because of the large radiation dose the
sample is greatly darkened after a few seconds of irradiation. The images in Fig. 4 at times 3.99 and 5.76
s have been filtered and processed to reduce noise and
enhance contrast to bring out the Kerr effect fringes
obscured by the darkening due to radiation damage.
/tEm1=2.0.
As shown in Figs. 3 and 4, the peak electric field is
of order 3Em:1.5 MV/cm at the top and bottom surfaces
while the peak volume charge density is roughly
q=d/dE1dkz3.9 C/m3. The total electric stress on the
sample is roughly
PeZec = 0.5 £[ E2(x=d) + E2(x=0)]
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z
7.4x105 N/M2
(3)
IEEE Transactions on Electrical Insulation Vol. EI-22 No.2, April 1987
4
to that in (3). Fig. 5 shows the mechanical birefringence optical pattern with and without weights for
aligned and crossed polarizers. We see that although
the stress distribution is slightly changed, multiple
fringes do not result so that the change in mechanical
birefringence is only a slight correction to the measurements of Figs. 3 and 4 when a large number of Kerr
electro-optic fringes are present.
Bea.m enarg 2.6 MIV
Current densityr220no/,m2
d
3 -~>
72
2 ~ r >*3
Thickness
1.27cm
Em 0.5 MV/cm
E/EEm
0
-4
89s
:uAdo" ocurd
-2
-3
m
01
irradiartion
3 99
5;76s
02 03 04 05 06 0.7 0.9 09
x/d
I.C
I
EmI
ight
i1.0
x/d
r
*
(**
L_
-_-
u
-
Fig. 5: Mechanical birefringence patterns with and
without applied mass of 110 kg for 1.27 cm thick
samples with dimensions 5.7 cm by 5.7 cm (32. 7 cm2
area). The applied pressure with the weight is
-
3.3xlOs N/M2.
Fig. 4: Normalized electric field E/Em and charge
density Jqd/(cEm)j for the three images shown at
various times as a fwnction of normaZized position
x/d for 1.27 cm thick PMVA, electron beam irradiated at 2.6 MeV energy and 220 nA/cm2 current density at various times before electric breakdown
after z6 s of irradiation. The coalescence of the
n=O and n=+1 lines at x/dz.44 results in the
sheet of surface charge with density Ia/sEm1=2.0.
The images shown have been filtered and processed
to reduce noise and enhance contrast to bring out
the Kerr effect fringes, obscured by the darkening
due to the radiation damage.
where ao3.7co for PMMA. To check if this high stress
of electrical origin could cause mechanical birefringence as well as electrical birefringence we placed z110
kg on an uncharged sample with area 32.7 cm2, creating
a mechanical pressure of
Pechz3.3xlc5 N/M2
ACKNOWLEDGMENTS
This work was supported by Computer Sciences Corporation, Albuquerque, NM, by a consortium of electric utility organizations as part of the M.I.T. Electric Utilities Program, by the National Science Foundation under Grants No. ECS-8517075 and by the Air Force Office
of Scientific Research. The photomultiplier tube traces
in Fig. 2 were taken by M.I.T. graduate student Thomas
Wang and M.I.T. Visiting Scientist Guang-Sheng Sun from
Academia Sinica, China.
REFERENCES
[1]
D. E. Cooper, T. C. Cheng, K. S. Kim and K.
Kantak, "Kerr Type Electro-Optic Effect In Solid
Dielectrics, IEEE Trans. Elect. Insul., Vol. El15, No. 3, pp. 294-300, 1980.
comparable
Authorized licensed use limited to: MIT Libraries. Downloaded on January 22, 2009 at 15:12 from IEEE Xplore. Restrictions apply.
Zahn et al.: Field mapping measurements in irradiated polymethylmethacrylate
[2]
K. S. Kim, T. C. Cheng and D. E. Cooper, "Kerr
Effect in Solid Polymethylmethacrylate and
Polyethylene," J. Appl. Phys., Vol. 54(1), pp.
449-451, 1983.
[3]
J. G. Trump and K. A. Wright, "Injection of
Megavolt Electrons into Solid Dielectrics,"
Mat. Res. Bull., Vol. 6, p. 1075, 1971.
[4]
W. W. Chang, "Trapping and Discharge of Megavolt
Electrons in Solid Dielectrics," M. S. Thesis,
Dept. of Elec. Eng., M.I.T., 1963.
[5]
C. M. Cooke, E. R. Williams and K. A. Wright,
"Electrical Discharge Propagation in SpaceCharged PMMA, " IEEE Intl. Symp. Electrical Insulation, Philadelphia, PA, p. 95, 1982.
*M.I.T. Visiting Scientist from Department of Electrical Engineering, Nagoya University, Japan.
This paper was presented at the 2nd International
Conference on Conduction and Breakdown in Solid
Lielectrics, ErZangen, Germany, 7-10 JuZy 1986.
Manuscript was received on 7 November 1986, in
revised form 2 February 1987.
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