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Influence of Field Spacer Geometry on the 
Performance of a High Voltage Coaxial Type 

Transmission Line with Solid Dielectric Spacer in 
Vacuum 

A. P. Anagha 
Electrical Engineering Department 
National Institute of Technology,  

Calicut, India 
 

K. Sunitha 
Electrical Engineering Department 
National Institute of Technology,  

Calicut, India 
karakkadsunitha@gmail.com

 

 

Abstract-With the development of more powerful high power 
electromagnetic sources, the transmission of high voltage power 
particularly between pulsed power systems to huge power rated 
microwave sources in absence of electrical breakdown and pulse 
distortion has begun to become a vital issue. A high voltage 
coaxial type transmission line with 500 kV peak voltage in 
vacuum is proposed. A novel proposal of configuration bearing a 
positive angle of 45o with socket-type filed shaper is being 
discussed in this paper in a manner to improve surface flashover 
properties and also to decrease the distortion seen in the pulse 
shape. This type of transmission line provides high capability of 
hold off voltage. The electric field distribution of the coaxial 
geometry with different field shaper configurations and different 
spacer parameters are also investigated using COMSOL 
software. 

Keywords-Field shaper; electromagnetics; surface flashover; 
triple junction; spacer; dielectrics. 

I. INTRODUCTION 
The development stages of electromagnetic radiation in the 

wave band regions of microwave and millimeter of 
electromagnetic spectrum began with the inception of pulsed 
power technology during the 1960s. The applications of such 
sources range from plasma physics to communication, some of 
which being particle acceleration techniques, fusion energy 
research, high-power radars, etc. [1-5]. The recent trends in the 
research area of High Power Electromagnetic Sources (HPEM) 
are basically due to the unmatchable advantages of being 
capable to deliver high average and peak power [6-8]. Recent 
trends showcased the development of still more powerful 
HPEM sources which geared the possibility of transmitting 
high voltage quasi-square pulses without causing any electrical 
breakdown. The stress upon electrical breakdown is a quite 
significant factor in coaxial transmission lines where surface 
flashover along the dielectric spacer surfaces occurs galore. 
Therefore, a more detailed study has to be done upon methods 
to deal with electrical breakdown and pulse distortion 
phenomenon, for delivering power efficiently along the high 
power transmission lines using pulsed power devices,.  

With proper alteration of the shapes of insulator and with 
the use of field shapers at triple junctions, significant reduction 
in surface flashover and dielectric breakdown has been 
observed. The conventional filed shaper designs are bump type, 
insertion type and the tangential type [9-13]. The main motive 
behind the installation of field spacers is to reduce the electric 
field strength seen at the triple junction where the electrode, 
dielectric and vacuum all come together. Even though they 
may seem successful in reducing the huge electric field 
strength seen at the triple junction, the field strength is not 
brought down to near zero due to imperfections in the field 
spacer design. Modification of insulator shape is done by 
proposing a new design of conical shaped insulator bearing an 
angle close to 45o and by increasing the length of surface of the 
insulator. 

Electromagnetic pulse is a short burst of electromagnetic 
energy that may be originated as a natural or a man-made  
radiated electric, conducted electric or magnetic field based on 
the source. The interference of EMP sources is very dangerous 
to electronic equipment, and high energy EMP sources such as 
lightning strikes can damage structures like buildings and 
aircrafts. The medium used to transfer these pulses are mainly 
grouped as guided and unguided media [4]. Guided media will 
provide a physical path to propagate the information, which 
includes twisted pair, coaxial cable and optical fiber. Unguided 
media uses an antenna to transmit the information through air, 
vacuum or water. For applications such as high speed local area 
network and high capacity long distance trunk etc., coaxial 
cables are used mostly because of their capability of higher 
data rates over long distances.  Hence, the most common type 
of antenna feeder used today is definitely coaxial cable. The 
common applications of coaxial cables include: transfer of 
radio frequency energy, domestic connections between 
receivers and aerials, carry any level of high frequency signals 
to any distance etc.  

Coaxial cable carries current through both inner and outer 
conductors, which are equal and opposite and as a result all the 
fields are confined within the cable. This is the basic principle 
of cable operation i.e. by propagating an electromagnetic wave 



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through it. The nearby objects are not affected by the 
interferences due to the absence of fields outside the coaxial 
cable. This is the main advantage of a coaxial cable compared 
to other forms. 

In this paper a new design of coaxial-type transmission line 
with socket type field shaper and a slight modification of the 
shape of the dielectric spacer is proposed to minimize the 
electric field strength and distortion of pulse. 

II. COAXIAL TYPE TRANSMISSION LINE 
The high power coaxial transmission line is composed of 

both inner and outer conductors, a solid dielectric spacer for 
supporting the inner structure, and also a field shaper. The 
conventional and proposed coaxial transmission lines are 
shown in Figure 1.  

A. Basic Design 

Generally, parameters for the coaxial transmission line are 
based on other factors such as the strength of breakdown field 
and impedance. Ideally, when losses are neglected, the field 
distribution pattern inside the coaxial line and also the 
characteristic impedance are expressed as [3]:   

( )

ln( )
r

v t
E

D
r

d

=               (1) 

ln( )
2

coax
r

D
Z

d
h

p e
=        (2) 

where r is the radius (d/2≤r≤D/2 ), v(t) is the applied 
voltage, d and D are the inner and outer diameters of the 
coaxial line, η is the intrinsic impedance, and εr is the relative 
permittivity of the material filling the space between the 
conductors. As keeping the objective to reduce the electric field 
strength, it is required to increase the outermost diameter of the 
coaxial line since the electric field is inversely proportional to 
the radius r. Also, coaxial impedance is proportional to the 
ratio of the diameter of the inner and outer conductors but 
inversely proportional to the dielectric permittivity. This makes 
it necessary to decrease the inner diameter of the coaxial line in 
order to get an impedance match between the spaces filled with 
air and dielectric. 

B. Surface Flashover Phenomenon 

Insulators ranges in various dimensions are used to 
supplement the system with potential variations under certain 
circumstances. This makes the role of High-Voltage hold off 
capability in insulators to be a vital one vastly in case of 
practical applications. Vacuum gap will have, mostly, an edge 
over the solid insulators (of comparable dimension) while 
considering their High Voltage hold off capacity. The 
phenomenon of surface discharge can be explained using three 
different phases: (a) Initiation Phase, (b) Growth Phase, and 
finally, (c) Final Phase. The instigation of the flashover occurs 
greatly by the discharge of electrons from the surface of a 
conductor under the influence of a strong electrostatic field, as 

a result of tunnel effect, which we call the whole process as 
Initiation Phase. A very few times, the cause for emission of 
electrons maybe due to a bunch of electrons or ions hitting the 
surface of the insulator. There still lies an ambiguity regarding 
the clarity of explanation for the next phase of event resulting 
in the growth of discharge, other than a few widely acclaimed 
interpretations. Most researchers prefer the process of 
secondary electron emission avalanche mechanism to explain 
the Development Phase, where a few of the already presen 
t(emitted) electrons may hit the surfaces and walls of the 
insulator thereby adding much more electrons into play by 
secondary emission. This process will continue thus 
agglomerating the continuously producing electrons to form a 
series connection of string of electrons called as Secondary 
Electron Emission Avalanche (SEEA) which is a possible 
reason for a complete flashover [5].   

 

 

 

Fig. 1.  Coaxial type transmission lines: (a) coaxial geometry with bump-
type field shaper, (b) coaxial geometry with socket-type field shaper 

The use of High Voltage Vacuum Insulators is mainly in 
pulsed power generators for the separation of dielectric and 
vacuum. The vacuum dielectric can be broadly classified as: 
insulator stack and coaxial insulator; while the commonly used 
one is the second type mostly in Tesla-type pulse power 
generator. Our concern in this type of generator is the 
insulation difficulties which may even lead to the final rupture 
of vacuum dielectric. The breakdown mechanism can be well 
reasoned by the aforesaid theory of secondary electron 
emission avalanche. The breakdown point in the triple junction 
is shown in Figure 2. The flashover may also be initiated due to 
anode side electrons at anode triple junction due to which 
flashover may occur at the surfaces in a predominantly high 
electric field. This may further increase the electric field 
intensity on the dielectric surface thus resulting in a huge 
rupture. This breakdown will build up across the surface on the 
way towards cathode until the flashover becomes complete [6]. 
Rather than the dependence alone on the magnitude of the 
applied voltage, the flashover voltage will greatly depend upon 
the size and waveform of the voltage. Likely, predominantly 
short pulses of nanosecond duration will have the highest 
flashover voltage while the comparatively longer pulses of 
microsecond duration and also DC pulses will have a medium 

(a) 

(b) 



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level of magnitude and AC voltages will be showing the lowest 
level of magnitude for flashover voltages. The complete time 
duration of flashover phenomenon depends on the time to 
initiate while the growth duration will be contributing very less 
to the total time duration. In addition to the waveform 
dependence of the flashover voltage, the shape and size of 
insulator will also exhibit a significant effect on the surface 
breakdown. Lastly, the type of material also greatly affects the 
surface flashover phenomenon. Generally, homogenous 
materials on top of non-homogeneous materials are preferred. 

 

 

Fig. 2.  The breakdown point at the CTJ (Cathode Triple Junction) 

III. DESIGN OF HIGH POWER COAXIAL GEOMETRY 
Different configurations of the coaxial type transmission 

line are discussed mainly the bump-type and socket type filed 
shaper design. The materials used for conductor, dielectric 
spacer and their relative permittivity are shown in Table I. 
Vacuum is used as the dielectric between the inner and outer 
conductor. The inner and outer conductor diameters are taken 
as 102 mm and 310 mm respectively [2].                  

TABLE I.  MATERIAL SPECIFICATIONS 

Part Material Used Relative permittivity 
Conductor Stainless steel 1 

Dielectric Spacer Nylon 66 3.2 

A. Design of the Bump- type Field Shaper 
The configuration of the bump-type field shaper is shown in 

Fig. 3. Here, the place for field shaper is around the area of the 
CTJ where the electrode and dielectric join in the vacuum [7]. 
This minimizes huge electric field strength experienced around 
the space. The dielectric spacer is realized using a coaxial type 
geometry bearing an angle of 45o to reduce the electric field 
seen on the dielectric spacer surface. 

 

 
Fig. 3.  Configuration of the Bump type field shaper design MT /MX=0.096, 

B/A=0.843 

B. Design of Socket - type Field Shaper 
Figure 4 shows the improved high power geometry with 

socket-type field shaper. This is used to make the electric field 
strength value to almost zero at the CTJ. The main advantage 
of this field shaper in comparison with the conventional one is 
that this can conceal the CTJ effectively and also thus it can 
eliminate the emission seed electron starting at the CTJ. A 
slight modification of the coaxial type dielectric spacer bearing 
a positive angle of 45o  is done at both ends to enhance the 
support provided to both inner and outer conductors. This 
modification also makes it advantageous by effectively 
shielding the cathode structure and therefore keeps away the 
dielectric surface from the huge electric field around the region 
of the cathode field shaper. 

 

 

 
Fig. 4.  Coaxial solid dielectric spacer MT/MX=0.079, HY/HX=1.9 and 

(b)socket type field shaper with Fx/Fy=0.375, FG/FY=0.25 

C. Modified Design of Socket type Field Shaper 
A modified design of the socket type field shaper is 

proposed in this paper to reduce the electric field mainly at the 
portion where the dielectric spacer and outer conductor meet. A 
socket type field shaper is used at CTJ. Instead of conical 
shaped dielectric with a positive angle of 45o a curved shape 
spacer is used. The proposed design is shown in the Figure 5. 

 

 

Fig. 5.  Modified design of socket type field shaper: Fx/Fy = 0.375, 
FG/FY=0.25, MT /MX = 0.179 and curved shape spacer 

IV. ANALYSIS OF HIGH POWER COAXIAL GEOMETRY 
To compare and verify the conventional and proposed high 

power coaxial geometry, simulation of different designs are 
carried out using the COMSOL MULTIPHYSICS software. 

(a) 

(b)



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Electrostatic analysis of the different configuration is 
performed. An excitation of 500 kV is applied to the inner 
conductor and the outer conductor is grounded. 

 

 
Fig. 6.  Electric field distribution of Bump type field shaper 

The electric field distribution of the bump type and of the 
socket type design is shown in Figures 6 and 7 respectively. 
The electric field distribution of socket type field shaper is 
more uniform compared to bump type field shaper along the 
coaxial solid dielectric. The bulged shape of the bump type 
field shaper makes the distribution more non-uniform and 
larger electrical stress is experienced in these regions. 

 

 
Fig. 7.  Electric field distribution of Socket type field shaper 

A. Analysis of Bump type Design 
The dimensions of the bump shape are varied and the 

electric field distribution is observed.  It is analyzed that as the 
bulged shape of the bump decreases, the electric field strength 
on its surface decreases and it becomes more uniform also.  
The simulation results are given in Figure 8. We can clearly 
observe from the results that, the intensity of the shape of 
bumpiness and the electric field strength are inversely 
proportional. 

B. Analysis of Socket type Design 
The bulged shape is completely removed and a new type of 

design called socket type design is proposed.  

1)  Effect of Spacing Width of Socket 
 The spacing width of the socket is varied and the electric 

field distribution is simulated which is shown in Figure 9. It is 
observed that a large variation in field distribution is not 
observed while varying the spacing, but a slight increase in the 
field strength as spacing decreases is analyzed. Spacing 
dimensions affect least importantly in the case of analysis of 

the electric field strength and they pose minimum threat to the 
design scenario with regard to electric field strength. But 
always a minimum spacing has always to be maintained for 
safer field strength levels.  

 

 
Fig. 8.  Analysis of bump type design 

2)  Effect of radius of the socket 
The radius of the socket is also varied and observations are 

shown in Figure 10.As the radius of the socket decreases a 
large increase in the electric field strength is observed. Electric 
field strength and the socket radius length are again inversely 
proportional and therefore the radius has to be maintained at a 
safe level so as to reduce the effect of high electric field 
strength at that region. 

C. Analysis of Proposed Modified Design 
From comparison, it is observed that electric field 

distribution on the surface of the cathode filed shaper is 
reduced to a large extend in case of socket type field shaper 
design. But both geometries have high electric field strength at 
the portion of dielectric spacer which meets the outer 
conductor. In order to overcome this drawback a modified 
spacer design of socket type field shaper coaxial geometry is 
proposed. The electric field distribution of the proposed design 
is given in Figure 11. A moreover uniform electric field 



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distribution is achieved by using the modified design of 
coaxial geometry. The simulation results for various 
dimensions of the new design are given in Figure 12. From the 
results it is clear that spacer with wider gap has uniform field 
distribution. The other one has large field concentration at the 
portion where spacer and outer conductor meet. 

 

 
Fig. 9.  Variation of Electric field with spacing of the socket 

 

 
Fig. 10.  Variation of electric field with radius of the socket 

 
Fig. 11.  Electric field distribution of the modified design 

 

 

Fig. 12.  Electric field for the modified design of spacer 

D. Comparison of all designs 
Comparing the electric field distribution of bump, socket 

and modified designs, it is observed that field distribution is 
more uniform with socket type field shaper and circular shape 
dielectric spacer. The range of maximum electric field as well 
as the minimum electric field is least for proposed modified 
design. The electric field is highest for bump type geometry 
and least for the modified geometry. This fact is better 
illustrated in Table II. 

TABLE II.  RESULTS COMPARISON  

Field shaper geometry Dielectric spacer 

Difference between 
maximum and 
minimum field 

(MV/m) 
Bump type Rhombus type 91.7 
Socket type Rhombus type 74 

Proposed modified design Circular curved 6 

 

V. CONCLUSION 
A coaxial–type matched transmission line to transmit high 

power with reduced electrical breakdown and pulse distortion 
is proposed and analyzed. A comparison of different field 



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shaper designs is carried out and concluds that the socket type 
field shaper is more favorable. Finally a modification is done 
for the spacer shape in the socket type filed shaper design. This 
has the basic advantage of reducing the electric field at the 
position where both spacer and outer conductor meet.  This 
type of transmission line that can provide a significant 
reduction of electric field strength to near zero at the CTJ and 
also good pulse shape may be very useful for high voltage 
pulse power applications. 

REFERENCES 
[1] S. D. Korovin, V. V. Rostov, S. D. Polevin, I. V. Pegel, E. Schamiloglu, 

M. I. Fuks, R. J. Barker, “Pulsed power-driven high-power microwave 
sources”, Proceedings of the IEEE, Vol. 92, No. 7, pp. 1082-1095, 2004 

[2] R. Kichouliya, M. Joy Thomas, “Interaction of high power 
electromagnetic pulses with power cables and electronic systems”, IEEE 
International Symposium on Electromagnetic Compatibility, Canada, 
July 25-29, 2016 

[3] J. Choi, Y. Kim, J. So, “Design of low distortion high voltage coaxial-
type transmission line for quasi-square wave nano-pulse with several 
hundred kilovolts in vacuum”, IEEE Transactions on Dielectrics and 
Electrical Insulation, Vol. 22, No.4, pp. 1809 – 1814, 2015 

[4] S. F. Mahmoud, Electromagnetic waveguides: theory and applications, 
IET, 1991 

[5] H. C. Miller, “Surface flashover of insulators”, IEEE Trans. Electr. 
Insul., Vol. 24, No. 5, pp. 765–786, 1989 

[6] L. Zhao, J.-C. Peng, Y.-F. Pan, X.-B. Zhang, J.-C. Su, “Insulation 
analysis of a coaxial high-voltage vacuum insulator,” IEEE Trans. 
Plasma Sci., Vol. 38, No. 6, pp. 1369–1374, 2010 

[7] J. Choi, Y. Kim, J. So, “Design and experiments of the 600 kV coaxial-
type matched divider for high-power microwave source array”, IEEE 
Trans. Electron Devices, Vol. 61, No. 12, pp. 4240–4246, 2014 

[8] L. G. Christophorou, R. V. Van Brunt, J. K. Olthoff, “Sulfur 
Hexafluoride and the electric power industry”, IEEE Electrical 
Insulation Magazine, Vol. 13, No. 5, pp. 20-24, 1997 

[9] L. Niemeyer, F. Y.Chu, “SF6 and the atmosphere”, IEEE Transactions 
on Electrical Insulation, Vol. 27, No. 1, pp. 184-187, 1992 

[10] L. G. Christophorou, R. V. Van Brunt, “SF6 /N2 mixture basic and HV 
insulation properties”, IEEE Transactions on Dielectrics and Electrical 
Insulation, Vol. 2, No. 5, pp. 952-1003, 1995 

[11] T. Nitta, Y. Shibuya, Y. Fujiwara, Y. Arahant, H. Takahashi, H. 
Kuwahara, “Factors controlling the surface flashover in SF6 gas 
insulated systems”, IEEE Transactions on Power Apparatus and 
Systems, Vol. PAS-97, No. 3, pp. 959-965, 1978 

[12] T. S. Sudershan, R. A. Dougal, “A review of mechanism of surface 
flashover along solid dielectrics in compressed gases”, IEEE 
Transactions on Electrical Insulation, Vol. EI-21, No. 5, pp. 727-746, 
1986 

[13] J. A. Bakken, “Determination of characteristics of voltage in impulse 
and switching surge testing”, IEEE Transactions on Power Apparatus 
and Systems, Vol. PAS-86, No. 8, pp. 962-968, 1967