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Coaxial cascade-line pulsed-power generator
Liang Zhao 1,2,* and Yue Wu 1,2,3
1Northwest Institute of Nuclear Technology,Xi’an, Shaanxi 710024, China
2Key Laboratory of Advanced Science and Technology on High Power Microwave,
Xi’an, Shaanxi 710024, China
3Department of Engineering Physics, Tsinghua University, Beijing 100084, China
(Received 29 November 2024; accepted 19 February 2025; published 17 March 2025)
The concept of the coaxial cascade-line rectangular-pulse generator is put forward, the basic idea of
which is to cascade two coaxial lines of equal impedance together and make one line turn around to let the
two lines use a common middle tube. The obvious feature of this kind of generator is that it can form a
rectangular pulse with a width of 4 times the electrical length of one line. Compared with the conventional
single-tube generator, the total stored energy is doubled. Namely, the output pulse width of the coaxial
cascade-line generator is doubled for the same output voltage, which is beneficial for miniaturization. The
principle of the cascade pulse forming line is first introduced; then the coaxial cascade-line rectangular-
pulse generator is suggested. The simulation results prove the feasibility of the cascade-line generators.
Finally, the design of a Tesla-type generator with an output power of 20 GW and a pulse width of 40 ns is
presented based on the coaxial cascade-line method.
DOI: 10.1103/PhysRevAccelBeams.28.031601
I. INTRODUCTION
A long-pulse power generator is an important direction
of the pulsed power technology. Generating a pulse with a
length of tens to one hundred nanoseconds (ns) is not only a
requirement of high power microwave (HPM) technology
[1] but also a requirement of Z-pinch technology [2,3]. The
conventional method to produce a rectangular pulse is to
use the pulse forming line (PFL) filled with an insulation
liquid such as transformer oil. The typical ones are the
Tesla-type generators in Russia [4,5] and China [6–9],
which can produce ideal nanosecond pulses. Figure 1gives
the schematics and the equivalent circuit of this kind of
generator, which include a PFL with a built-in Tesla
transformer (represented with Z1), a transmission line
(TL, represented with Z1) with an equal length of the
PFL, a switch, and a load, where Z1and Z2are the
characteristic impedance of the PFL and the TL, respec-
tively. The feature of this type of generator is that 1-m
transformer-oil-insulated PFL can form a 10-ns pulse width
(¼1m÷3×108m=s×2×2.250.5) since the relative
dielectric constant of transformer oil is 2.25. So, if a
100-ns rectangular pulse is required, the PFL should be
10 m. Since the length of the TL should be equal to that
of the PFL, the total length of the 100-ns generator should
be at least 20 m. Here is an example, the total length of
the famous Sinus-7 is 12 m with an output pulse width of
50 ns [10]. If the output pulse is doubled to 100 ns, the total
length would be also doubled to at least 24 m. This may be
acceptable in a lab but is unacceptable for industrial
applications.
In view of this, several methods were invented to
elongate the pulse width with a shorter PFL.
The first method is to replace the transformer oil with an
insulation liquid of a higher relative dielectric constant.
For example, the deionized water, with an εrof 81, can
conspicuously broaden the pulse width by nearly 6 times,
since ðεrwater=εroil Þ0.5¼ð81=2.25Þ0.5¼6.However,the
water needs to be cycled periodically to keep the resis-
tance. The typical generators of this kind can be found
in Ref. [11].
The second method is to use pulse pulse-forming net-
work (PFN). The PFN is as a matter of fact a batch of
capacitors connecting in series and parallel. The waveform
is usually not as flat as that of a coaxial line. The typical
generators of this kind can be found in Refs. [12–14].
The third method is to use the spiral line as part of the
inner conductor of the PFL. The typical generator is the
Sinus-700=130, which can produce a pulse with a width of
130 ns for a total length of 6 m. More details can be seen in
Refs. [4,15–17]. Some Blumlein-type generators also took
this kind of technology to increase the pulse width [18–20].
The fourth method is to roll the thin film on a special
inner conductor and to connect several stages of the thin-
film modulator together in series to form a shorter PFL.
*Contact author: zhaoliang@nint.ac.cn
Published by the American Physical Society under the terms of
the Creative Commons Attribution 4.0 International license.
Further distribution of this work must maintain attribution to
the author(s) and the published article’s title, journal citation,
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PHYSICAL REVIEW ACCELERATORS AND BEAMS 28, 031601 (2025)
2469-9888=25=28(3)=031601(10) 031601-1 Published by the American Physical Society
Each stage of the thin-film modulators is similar to each
stage of a PFN. However, the top of the output waveform is
much flatter than that of PFN due to the uniformity of the
film [21–23].
Recently, the technology of double-width pulse-forming-
line (DW-PFL) technology was put forward by Zhang et al.
[24], which can double the pulse width by introducing a
middle tube between the outer and the inner conductors of
the PFL without increasing the total length of PFL. The
typical generator of this kind was invented by Zhang et al.,
which can be found in Refs. [25–27] and can also be found
in Ref. [28] by Rostov et al.
All these methods can effectively increase the pulse
width of the Tesla-type generators. But each method has its
own advantages and disadvantages. If evaluated from the
perspective of gain and loss, the DW-PFL technology is
more economical and creative, since it can generate a 20-ns
pulse with 1-m oil-filled PFL. However, the space between
the middle and the outer conductor is not charged during
the charging process, which wastes the space and results in
a lower stored energy.
Aside from these methods, the folded PFL was intro-
duced in Ref. [29]. With this method, a longer pulse can be
formed with a much shorter PFL, which saves space.
However, this method was only applied to the planar pulse
generator. There is no report on the application of this
method to coaxial pulse generators.
In this paper, the concept of coaxial cascade-line
rectangular-pulse generator is put forward, the basic prin-
ciple of which is to cascade two lines together in the radial
direction and let one line turn around. The obvious feature
of this kind of generator is that it can not only form a 20-ns
pulse with 1-m oil-filled PFL in axial length but also double
the stored energy. Following this, Sec. II introduces the
basic principle of this kind of generator. Section III deals
with the simulation of the planar cascade-line generator.
Section IV copes with the simulation on the coaxial
cascade-line generator. Section Vpresents the design of
a 20-GW Tesla-type cascade-line generator. Section VI
presents the conclusions of this paper.
II. BASIC PRINCIPLE
A. Equivalent circuit
Figure 2shows the equivalent circuit of the cascade-line
generator. Compared with that of the traditional Tesla-type
generator in Fig. 1(b), only the switch is moved to connect
in series with the load, R. In this way, line 1 (which is also
Z1) is cascaded to line 2 (which is also Z1). More
importantly, line 2 is folded back to decrease the total
length of the generator, as shown in Fig. 3. In Fig. 3(c), the
two lines use a common conductor B’E. It is noted that Z1
should be equal to Z2since Z1and Z2are in nature one PFL
sharing the same impedance. In the following paragraph,
Z1is defaulted to be Z2.
FIG. 2. Equivalent circuit of unfolded cascade-line rectangular-
pulse generator.
FIG. 1. Schematics of typical Sinus-series pulsed power generators (a) and their equivalent circuit; (b) 1-PFL with a built-in Tesla
transformer; 2-gas spark switch; 3-transmission line; 4-load. Z1the characteristic impedance of the PFL, which represents the first line;
Z2the characteristic impedance of the TL, which represents the second line.
LIANG ZHAO and YUE WU PHYS. REV. ACCEL. BEAMS 28, 031601 (2025)
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When the conductor AD is charged to V0and the switch
is closed, a rectangular pulse can be formed on R. The
obvious feature of this kind of generator is that it can form a
rectangular pulse with a width of 4 times the electrical e
length of one line. In other words, this method halves the
total length of the generator. Therefore, it can be used for
the miniaturization of GW-class pulsed power generators.
B. Basic wave process
Assume that the length of both the lines is l, the electrical
length of each line is τ, the switch is ideal, and the
impedance of each line is ZðZ¼RÞ, then the amplitude
of the wave formed on Ris:
VR¼V0
R
RþZ¼V0
2:ð1Þ
The wave process of the cascade-line rectangular-pulse
generator can be described as follows:
In 0∼2τ, a pulse with an amplitude of −V0=2transmits
from line 2 to line 1. The voltage of the lines where the pulse
has passed would decrease to V0=2, as shown in Fig. 4(a).
At 2τ, this pulse meets the left end of line 1 and changes
its direction. All the voltage of the two lines decreases to
V0=2at this time.
In 2τ∼4τ, this pulse transmits from line 1 to line 2. The
voltage of the two lines where the pulse has passed
decreases to 0, as shown in Fig. 4(b).
At 4τ, the end of this pulse arrives at the right end of
line 2. All the voltage of the two lines decreases to 0, as
shown in Fig. 4(c). The wave process finishes.
Finally, a pulse with amplitude of V0=2and a width of
4τis formed on the load R. The final waveform is shown
in Fig. 4(d).
If Figs. 3(c) and 4(d) are combined together, it can be
concluded that the cascade-line pulse generator can produce
a4-τrectangular pulse only with one PFL’slengthofl.
It is worth mentioning that the basic elements in Fig. 3(c)
are the same as those in Fig. 1(b), which are two lines, one
load and one switch. But both the two lines in Fig. 3(c)
serve as PFL whereas only line 1 in Fig. 1(b) serves as PFL.
So, the stored energy is doubled and the output pulse width
is doubled too in Fig. 2. This is the advantage of the
generator in Fig. 2. This method can be applied to the Tesla-
type generator to solve the problem of incompactness to a
certain extent.
III. APPLICATION INTO PLANAR LINE
The principle of the cascade line is first applied to the
planar line. Two models are constructed and compared: an
FIG. 3. Equivalent circuit of the folded cascade-line rectangular-pulse generator. (a) Mediate type; (b) folded type; (c) planar cascade-
line generator.
FIG. 4. Wave process of the cascade-line rectangular-pulse generator. (a) 0∼2τ; (b) 2τ∼4τ; (c) t>4τ; (d) final waveform.
COAXIAL CASCADE-LINE PULSED-POWER …PHYS. REV. ACCEL. BEAMS 28, 031601 (2025)
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unfolded and a folded type; both of which are shown
in Fig. 5.
The parameters of the two models are as follows:
(i) Widths of two lines: w¼600 mm; (ii) Distance of the
planes of the two lines: d¼60 mm; (iii) Lengths of two
lines: l¼3000 mm; (iv) The two lines are insulated by gas.
So the impedance, Z,is37.7Ωbased on the following
formula:
Z¼377 d
w;ð2Þ
(v) The electrical length, τ, of each line is about 10 ns based
on the following formula:
τ¼l
c;ð3Þ
where cis the light speed and is equal to 3×108m=s.
A professional electromagnetic simulation software,
Computer Science Technology is used to analyze the wave
process of the two models. This kind of software cannot only
simulate the static electromagnetic field distribution in HV
devices but can also simulate the transient wave processes
such as the discharging process. In this model, the charging
voltage is 1 V. The lumped load resistance is set 37.7Ω.
Figure 6shows the final waveform on the loads. From this
figure, it is seen that rectangular pulses are produced by both
the two planar cascade-line generators; in addition, the
amplitude is about 0.5 V, which is just half of the charging
voltage. The pulsewidth is 41.29 ns. This value is basically 4
times the electrical length of a single line, i.e., 10 ns. These
two results agree with the theory in Sec. II.
It is noted that the latter half top of the folded planar
cascade-line generator decreases by 0.014 V. This is due to
the folding positions of the generator. However, the
decrement is only 3% of the total amplitude of the main
waveform, which is acceptable.
IV. COAXIAL CASCADE-LINE GENERATOR
A. Two sub-types
The cascade-line principle can be applied to the Tesla-
type generator to decrease the length of the PFL. Basically,
there are two subtypes of the coaxial cascade-line pulse
FIG. 5. Two models of the planar cascade-line generators. (a) Unfolded type; (b) folded type.
FIG. 6. Comparison of the waveforms of two types of planar cascade-line generators.
LIANG ZHAO and YUE WU PHYS. REV. ACCEL. BEAMS 28, 031601 (2025)
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generators based on Fig. 3(c). The first one has the load and
the switch located between the middle and the inner tubes,
as shown in Fig. 7(a); the second one has the switch and
load located between the middle and the outer tubes, as
shown in Fig. 7(b).
As to the load-located-in sub-type, it is difficult for
engineering realization not only because the inner space is
small but also because the output waveform is hard to
introduce to the outside of the generator.
As to the load-located-out sub-type, the load is directly
connected to the outer tube, which is easy to realize. In
addition, the switch is easy to assemble. So, this subtype is
of practical value.
B. Transient simulation
The 3-D model of a coaxial load-out coaxial cascade-line
pulse generator is constructed, which is shown in Fig. 8.
The basic parameters of this generator are as follows:
(i) Diameter of inner conductor: din ¼72 mm; (ii) Inner
diameter of middle conductor: dmid1¼195 mm; (iii) Outer
diameter of middle conductor: dmid2¼200 mm; (iv) Diameter
of outer conductor: dout ¼544 mm; (v) The axial length of all
the three tubes: l1¼3300 mm; (vi) The axial length of the
transmission line: l2¼600 mm. (vii) All the space is gas-
insulated. So, the impedance of the two lines, Z’,is60 Ωbased
on the following formula:
FIG. 7. Two types of coaxial cascade-line generators. (a) Switch and load located between the middle and the inner tubes and
(b) switch and load located between the middle and the outer tubes. The middle tube should be charged with different polarity if a
positive pulse is desired.
FIG. 8. Model of the coaxial cascade-line pulse generator with
built-out load. 1-inner conductor; 2-middle conductor; 3-outer
conductor; 4-charger; 5-switch; 6-load. The inner conductor and
the middle conductor form the line 1; the outer conductor and the
middle conductor form the line 2.
COAXIAL CASCADE-LINE PULSED-POWER …PHYS. REV. ACCEL. BEAMS 28, 031601 (2025)
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Z0¼60
ffiffiffiffi
εr
pln dmid1
din ¼60
ffiffiffiffi
εr
pln dout
dmid2
;ð4Þ
where εris the relative dielectric constant of air and is equal to
1. (viii) The electrical length of the two lines, τ0,is11nsbased
on the following formula:
τ0¼l1
c.ð5Þ
Similarly, the transient field-circuit mixed simulation
software is used. The charging voltage on the middle
conductor is set as 1 V. The lumped load resistance is set as
60 Ω. Figure 9shows the output waveform on the load.
From this figure, it is seen that a rectangular pulse is
produced. The amplitude is about 0.5 V, nearly half of the
charging voltage. The pulse width is 52.289 ns, basically 4
times the 11-ns electrical length of one line. These two
results basically agree with the theory. It is noted that the
pulse width of 52.289 ns is longer than the theoretical value
of 44 ns. This is because of the front and back covers of the
coaxial lines since energy is also stored in these regions.
It is noted that if compared with the waveforms of the
planar cascade-line generators in Fig. 6, the waveform of
the coaxial cascade-line generator in Fig. 9has a much
“slower”rise time and fall time. The slowdown of the rise
time is due to the large capacitance of the switch; the
slowdown of the fall time is due to the large capacitance in
the left end of the inner conductor.
The simulation shows that the coaxial cascade-line pulse
generator does double its output pulse width. This is due to
the double of the stored energy. However, the coaxial
cascade-line generator has an obvious shortcoming, i.e.,
both line 1 and line 2 are charged for a long time to the
maximum voltage, V0, in the charging process. So the
insulation between the middle and the inner conductors
mainly limits the whole insulation ability of the PFL since
the electric field on the surface of the inner conductor may
increase at least by dout=dmid2times.
In order to solve this question, solid dielectric with high
insulation ability can be used. For example, the polypropyl-
ene (PP) film can be wounded on the inner conductor and
then can be inserted into the single-tube generator to keep the
radial size of the generator the same. The breakdown field of
PP film is in MV/cm class whereas the operation field of the
insulation gas like SF6or the insulation liquid like trans-
former oil is only 100–300 kV=cm. So, this solution way is
feasible.
V. DESIGN OF A 20-GW COAXIAL
CASCADE-LINE GENERATOR
A. Early work
A pulsed power generator with parameters of an output
power of 20 GW and a pulse width of 40 ns is expected for
high power microwave (HPM) generation in our lab. In
2011, a Tesla-type generator with such parameters was
developed. This generator adopted the conventional single-
line PFL technology with a TL, the schematic of which is
the same as that shown in Fig. 1. The diameter of this
generator is about 1 m; the total length is about 10 m. More
details of this generator can be found in Ref. [30]. Such a
long generator does not meet the miniaturization require-
ment. So, a generator having the same parameters but a
much more compact size is urgently required. To shorten
the total length, the TL of this generator can be cut off first.
Then, the coaxial cascade-line technology can be used to
further decrease the total length. This is a general consid-
eration. Proof-of-principle experiments were also conducted
on a 100-kV Tesla-type spiral-line pulse generator. More
details can be found in Refs. [20,25].
As for practical design, generally, there are two main
steps. The first step is the design of the coaxial cascaded
PFL; the second step is the design of the Tesla transformer,
which is used to charge the PFL.
FIG. 9. Simulated output waveform of the coaxial cascade-line pulse generator with built-out load.
LIANG ZHAO and YUE WU PHYS. REV. ACCEL. BEAMS 28, 031601 (2025)
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B. Design of coaxial cascaded PFL
The general 3-D model of this coaxial 20-GW cascade-
line generator can be referred to as that shown in Fig. 8.
Transformer oil with an εrof 2.25 is used as the insulation
medium, which is the same as that for the previous 20-GW
generator. The circuit schematic of this generator is shown
in Fig. 10. The impedance of line 1 and line 2 is both set to
40 Ω, which is the same as that of the previous 20-GW
generator. It is noted that the PFL in this model reflects both
the inner and the outer PFLs of the cascade line.
With the output power Pof 20 GW and the load
impedance Zdof 40 Ω, the output voltage on load, Ud,
is calculated as follows:
Ud¼ffiffiffiffiffiffiffiffiffi
PZd
p¼0.894 MV. ð6Þ
A single-gap gas-switch is used as the main switch, the
equivalent resistance, Rs, of which is set as 8Ω. Based on
Fig. 10(b), the charging voltage of the PFL, U0, can be
calculated as follows:
U0¼Ud
ZdþRsþZPFL
Zd¼1.968 MV;ð7Þ
where ZPFL ¼Z1¼Z2¼40 Ω. The ratio of the inner
diameter of the outer tube to the outer diameter of the
middle tube, dout=dmid1, for line 1 and the ratio of the inner
diameter of the middle tube to the outer diameter of the
inner tube, dmid2=din, for line 2 can be calculated as follows:
dout
dmid1¼dmid2
din ¼exp 60
ZPFL ffiffiffiffi
εr
p¼e; ð8Þ
where εr¼2.25. Taking into account that the stable
operating electric field, Emax, of transformer oil is
100 kV=cm, the value of dmid1can be calculated as follows:
dmid1¼2U0
Emax ln dout
dmid1¼394 mm. ð9Þ
So, dout ¼dmid1×e¼1070 mm. The thickness of the middle
tube is set as 25 mm. So, dmid2is 344 mmð¼ 394 −25 ×2Þ.
In turn, din is calculated to be 126 mmð¼ 344=eÞ.Then,the
maximum field, Emax0, on the outer surface of the inner tube
would be
Emax0¼U0
din
2ln dmid2
din ¼311 kV=cm. ð10Þ
This field is so strong that exceeds the breakdown field
of transformer oil (∼300 kV=cm). As aforementioned in
Sec. IV B, PP film can be used as the insulation medium.
PP also has an εrof 2.2, which is close to that of transformer
oil. So, the above calculation results still hold true. In addition,
there would be field enhancement in the junction of oil, PP,
and metal.
The stable operating field, Eop, is as large as 800 kV=cm
for a multilayered PP film with a thickness of 4.5 mm. Now
the thickness of the multilayered film is increased to
109 mmð¼ ð344 −126Þ=2Þ. This would lead to a decrease
in the stable operating field. The stable Eop of the thickness-
increased PP film is decreased to Eop0based on the
thickness effect on the breakdown field as follows [31]:
Eop0¼Eop ðd=d0Þ−1=8¼800 ×ð109=4.5Þ−1=8
¼537 kV=cm. ð11Þ
It is seen that Eop0is still larger than Emax 0of 311 kV=cm.
So, the insulation margin of the PP film is enough. It is
noted that the use of a solid dielectric has the disadvantage
of irreversibility when a breakdown occurs, i.e., its lifetime
is limited.
The total length of the PFL can be calculated as follows:
lPFL ¼τc
2ffiffiffiffi
εr
p¼4m;ð12Þ
where τ¼40 ns, cis the light speed equal to 0.3m=ns,
and εr¼2.25. The cascade-line technology can halve the
length of the PFL. So, the final length of the PFL, lPFL0,is
only 2 m. Table Ilists the key sizes of the PFL of the current
cascade-line 20-GW generator. Table Ialso compares them
with the key sizes of the previous single-line 20-GW
FIG. 10. Schematics of the 20-GW cascade-line generator. (a) Equivalent transmission line model. (b) Equivalent circuit.
COAXIAL CASCADE-LINE PULSED-POWER …PHYS. REV. ACCEL. BEAMS 28, 031601 (2025)
031601-7
generator. From Table I, it is seen that the two generators
have close outer diameters of PFL, but the length of the
cascade-line generator is only about 4.5 m, which is far
shorter than that of the single-line generator, which is 10 m.
Figure 11 also compares the schematic of these two 20-GW
generators.
C. Design of Tesla transformer
A Tesla transformer with open magnetic cores is still
used as the boosting voltage unit, which is the same as that
for the previous 20-GW generator. The secondary voltage
of the transformer, Us, which is also the PFL voltage, U0,is
set as 2 MV, a little larger than 1.938 MV. The turn number
of the secondary winding, ns, is set as 2800. The turn
number of the primary winding, np, is set as 1. So, the turn
number ratio of the secondary winding to the primary
winding, n, is 2800.
The secondary capacitance of the Tesla transformer, Cs,
can be calculated as follows:
Cs¼2πl0
PFLε0εr
ln dout
dmid1þ2πl0
PFLε0εr
ln dmid2
din ¼500 pF. ð13Þ
The equivalent secondary capacitance in the primary loop,
Cs0, can be calculated as follows:
Cs0¼n2Cs¼3.9mF. ð14Þ
The capacitance ratio of the primary capacitance to the
secondary capacitance, α, is set as 1.05. So, the primary
capacitance, Cp, can be calculated as follows:
Cp¼αCs0≈4.1mF. ð15Þ
The length of the secondary winding, lc, is set as 0.5lPFL0,
i.e., lc¼1000 mm. The length of the magnetic core, lm,
should be 200 mm shorter than lPFL0. So, lm¼1800 mm.
With rout ¼dout=2¼535 mm, β¼dout=dmid2¼2.727,
lm¼1800 mm, and lc¼1000 mm, the leak inductance,
Lsp, and the magnetization inductance, Lm, can be calcu-
lated as follows:
Lsp ¼μ0n2
pπr2
out
lc
ð2βþ1Þðβ−1Þ
3β2¼564 pF and
Lm¼πμ0n2
pðlm−lcÞ
2ln β¼1.58 μF. ð16Þ
The coupling coefficient, k, of the Tesla transformer can be
calculated as follows:
TABLE I. Key parameters of two types of 20-GW Tesla-type
generator.
Generator
Cascade-line
generator
Single-line
generator
dout 1070 1120
dmid2394 412
dmid1344 no
din 126 no
lPFL02000 4000
Length of TL 500 4000
Length of back cover,
switch, and load
2000 2000
Total length 4500 10000
FIG. 11. Comparison between the single-line Tesla-type generator and the cascade-line generator. 1-PFL with built-in Tesla
transformer; 2-gas switch; 3-transmission line; 4-vacuum diode.
LIANG ZHAO and YUE WU PHYS. REV. ACCEL. BEAMS 28, 031601 (2025)
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k≈1−
r2
out
ðlm−lcÞlc
ð2βþ1Þðβ−1Þln β
3β2¼0.821.ð17Þ
The equivalent capacitance, which is the series value of Cp
and Cs0, can be calculated as follows:
C¼CpC0
s
CpþC0
s¼2mF. ð18Þ
The characteristic impedance of the equivalent loop, Z, and
the charge time, tch, can be calculated as follows:
Z¼ffiffiffiffiffiffiffi
Lsp
C
r¼16.8mΩand tch ¼πffiffiffiffiffiffiffiffiffiffi
LspC
p¼105 μs.
ð19Þ
The total loop resistance, R, is estimated to be 1mΩ. So,
the normalized loop resistance, R=Z,is0.06ð¼ 1=16.8Þ.
With α¼1.05,k¼0.821, and R=Z ¼0.06, the normal-
ized voltage boosting factor, λ0, of this transformer can be
calculated as follows:
λ0¼Us=Up
n¼α
1þα1þexp−
πR
2Z−
π2αð1−kÞ
1þα
þπ2αð1−kÞ
1þα2¼0.931.ð20Þ
So, the voltage boosting factor, Us=Up, which is equal to
nλ0,is2604ð¼ 2800 ×0.93Þ. Since the secondary voltage,
Us, is 2 MV, the primary voltage, Up, should be no smaller
than 768Vð¼ 2MV=2604Þ. In addition, the theoretical
energy transmission efficiency, η, of the Tesla transformer
can be calculated as follows:
η¼λ2
0
α¼0.828.ð21Þ
By far, the key parameters of the Tesla transformer are all
obtained, which are listed in Table II.
With the values in both Tables Iand II,theexpected
coaxial cascaded-line 20-GW generator can be established.
Figure 12 gives the final design of the coaxial cascade-line
20-GW generator. From this figure, one can see that the total
length of this generator is much shorter than the previous
single-line generator (Φ1m×10 m) with the same output
parameters. So, the miniaturization goal is basically fulfilled.
VI. CONCLUSIONS
The concept of a cascade-line rectangular-pulse gener-
ator is put forward. The principle is to cascade two lines
with equal impedance and let one turn around to decrease
the axial length. Compared with the traditional single-line
Tesla-type generators, the total stored energy can be
doubled and the output pulse width can also be doubled.
This is highly beneficial for the miniaturization of the
pulsed power generators, especially for the Tesla-type
generators. There are two subtypes for the folded coaxial
cascade-line generators: one has the load and the switch
TABLE II. Key parameters of the Tesla transformer of the cascaded 20-GW generator.
Design parameters Mediate parameters
Parameter Value Parameter Value
Primary turn number, np1 Turn number ratio, n2800
Secondary turn number, ns2800 Capacitance ratio, α1.05
Secondary capacitance, Cs500 pF Equivalent secondary capacitance, Cs03.9 mF
Primary capacitance, Cp4.1 mF Equivalent capacitance, C2mF
Leak inductance, Lsp 563 nH Coupling factor, k0.82
Magnetization inductance, Lm1.58 μH Characteristic Impedance, Z16.8mΩ
Primary inductance, Lp¼Lsp þLm2.21 μH Total resistance, R(estimated) 1mΩ
Secondary inductance, Ls¼n2Lm12.38 H Normalized resistance, R/Z 0.0596
Normalized voltage boosting factor, λ0¼0.931
Energy transfer efficiency, η¼0.828
Charge time, tch ¼105 μs
FIG. 12. The final design of the coaxial cascade-line 20-GW
Tesla-type generator. 1, 2-secondary and primary windings;
3, 4-outer and inner magnetic cores; 5-PP film.
COAXIAL CASCADE-LINE PULSED-POWER …PHYS. REV. ACCEL. BEAMS 28, 031601 (2025)
031601-9
located between the inner and the middle tubes and the
other has the load and the switch located between the
middle and the outer tubes. Only the latter has engineering
feasibility. A 20-GW generator of this kind is designed. The
insulation of the outer line is realized via transformer oil
whereas the inner insulation is realized via PP films. The
total length of this generator is only 4.5 m for an output
pulse width of 40 ns, which is nearly half of the already-
constructed 20-GW Tesla-type generator.
ACKNOWLEDGMENTS
This work is supported by the National Natural Science
Foundation of China (NNSFC) under Grant No. 12175182.
DATA AVAILABILITY
The data that support the findings of this study are
available from the corresponding author upon reasonable
request.
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