Exciting high frequency oscillations in a coaxial transmission line with a magnetized ferrite: 2D approach
1D and 2D simulation methods and research into the formation of high frequency oscillations in a coaxial nonlinear transmission line (NLTL) partially filled with a longitudinally magnetized ferrite are presented. Dynamics and structure of the electromagnetic wave fields produced in the NLTL with a t...
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irk-123456789-1123552017-01-21T03:02:49Z Exciting high frequency oscillations in a coaxial transmission line with a magnetized ferrite: 2D approach Ahn, J.W. Karelin, S.Yu Krasovitsky, V.B. Kwon, H.O. Magda, I.I. Mukhin, V.S. Sinitsin, V.G. Новые и нестандартные ускорительные технологии 1D and 2D simulation methods and research into the formation of high frequency oscillations in a coaxial nonlinear transmission line (NLTL) partially filled with a longitudinally magnetized ferrite are presented. Dynamics and structure of the electromagnetic wave fields produced in the NLTL with a transverse inhomogeneity are studied for the first time within a 2D model. Means for optimizing the electromagnetic system parameters, NLTL dimensions, and degree of the line filling, needed to increase the electric strength and maximize oscillation intensity are discussed. Представлено методику та результати 1D- і 2D-чисельного моделювання процесу формування високочастотних коливань у коаксіальній нелінійній лінії, що частково заповнена феритом, який намагнічено повздовжнім магнітним полем. За допомогою 2D-моделі вперше досліджено динаміку та структуру хвильового поля нелінійної лінії з поперечною неоднорідністю. Обговорюється оптимізація діелектричних параметрів системи, розмірів лінії та ступеня її заповнення феромагнітним матеріалом, які необхідні для підвищення електричної стійкості та отримання максимальної інтенсивності коливань. Представлена методика и результаты 1D- и 2D-численного моделирования процесса формирования высокочастотных колебаний в коаксиальной нелинейной линии, частично заполненной ферритом, который намагничен продольным магнитным полем. С помощью 2D-модели впервые исследованы динамика и структура волнового поля нелинейной линии с поперечной неоднородностью. Обсуждается оптимизация диэлектрических параметров системы, размеров линии и степени ее заполнения ферримагнитным материалом, необходимых для повышения электрической прочности и получения максимальной интенсивности колебаний. 2015 Article Exciting high frequency oscillations in a coaxial transmission line with a magnetized ferrite: 2D approach / J.W. Ahn, S.Yu Karelin, V.B. Krasovitsky, H.O. Kwon, I.I. Magda, V.S. Mukhin, V.G. Sinitsin // Вопросы атомной науки и техники. — 2015. — № 6. — С. 68-72. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 41.20.jb, 75.30.Cr, 75.50.Bb http://dspace.nbuv.gov.ua/handle/123456789/112355 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Новые и нестандартные ускорительные технологии Новые и нестандартные ускорительные технологии |
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Новые и нестандартные ускорительные технологии Новые и нестандартные ускорительные технологии Ahn, J.W. Karelin, S.Yu Krasovitsky, V.B. Kwon, H.O. Magda, I.I. Mukhin, V.S. Sinitsin, V.G. Exciting high frequency oscillations in a coaxial transmission line with a magnetized ferrite: 2D approach Вопросы атомной науки и техники |
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1D and 2D simulation methods and research into the formation of high frequency oscillations in a coaxial nonlinear transmission line (NLTL) partially filled with a longitudinally magnetized ferrite are presented. Dynamics and structure of the electromagnetic wave fields produced in the NLTL with a transverse inhomogeneity are studied for the first time within a 2D model. Means for optimizing the electromagnetic system parameters, NLTL dimensions, and degree of the line filling, needed to increase the electric strength and maximize oscillation intensity are discussed. |
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Article |
| author |
Ahn, J.W. Karelin, S.Yu Krasovitsky, V.B. Kwon, H.O. Magda, I.I. Mukhin, V.S. Sinitsin, V.G. |
| author_facet |
Ahn, J.W. Karelin, S.Yu Krasovitsky, V.B. Kwon, H.O. Magda, I.I. Mukhin, V.S. Sinitsin, V.G. |
| author_sort |
Ahn, J.W. |
| title |
Exciting high frequency oscillations in a coaxial transmission line with a magnetized ferrite: 2D approach |
| title_short |
Exciting high frequency oscillations in a coaxial transmission line with a magnetized ferrite: 2D approach |
| title_full |
Exciting high frequency oscillations in a coaxial transmission line with a magnetized ferrite: 2D approach |
| title_fullStr |
Exciting high frequency oscillations in a coaxial transmission line with a magnetized ferrite: 2D approach |
| title_full_unstemmed |
Exciting high frequency oscillations in a coaxial transmission line with a magnetized ferrite: 2D approach |
| title_sort |
exciting high frequency oscillations in a coaxial transmission line with a magnetized ferrite: 2d approach |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2015 |
| topic_facet |
Новые и нестандартные ускорительные технологии |
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http://dspace.nbuv.gov.ua/handle/123456789/112355 |
| citation_txt |
Exciting high frequency oscillations in a coaxial transmission line with a magnetized ferrite: 2D approach / J.W. Ahn, S.Yu Karelin, V.B. Krasovitsky, H.O. Kwon, I.I. Magda, V.S. Mukhin, V.G. Sinitsin // Вопросы атомной науки и техники. — 2015. — № 6. — С. 68-72. — Бібліогр.: 7 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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ISSN 1562-6016. ВАНТ. 2015. №6(100) 68
EXCITING HIGH FREQUENCY OSCILLATIONS IN A COAXIAL
TRANSMISSION LINE WITH A MAGNETIZED FERRITE:
2D APPROACH
J.W. Ahn1, S.Yu Karelin2, V.B. Krasovitsky2, H.O. Kwon1, I.I. Magda2, V.S. Mukhin2, V.G. Sinitsin2
1Hanwha Corporation, Gumi, Kyungbuk, Korea;
2National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
E-mail: magda@kipt.kharkov.ua
1D and 2D simulation methods and research into the formation of high frequency oscillations in a coaxial
nonlinear transmission line (NLTL) partially filled with a longitudinally magnetized ferrite are presented. Dynamics
and structure of the electromagnetic wave fields produced in the NLTL with a transverse inhomogeneity are studied
for the first time within a 2D model. Means for optimizing the electromagnetic system parameters, NLTL
dimensions, and degree of the line filling, needed to increase the electric strength and maximize oscillation intensity
are discussed.
PACS: 41.20.jb, 75.30.Cr, 75.50.Bb
INTRODUCTION
Since 1960s, nonlinear phenomena arising when an
electrical current impulse travels through the transmis-
sion line partially filled with ferromagnetic media, have
been studied intensely - initially as a way to sharpen the
pulse rise-time and create electromagnetic shock waves
[1, 2]. Today, the attention of researchers is mostly fo-
cused to direct energy conversion from a short video-
pulse to high-frequency oscillations, which can be ex-
tracted from the structure in the form of intense HF ra-
diation [3 - 6]. This work is devoted to numerical study
of the process of formation HF oscillations in the NLTL
with a ferrite based on 1D and 2D theoretical models
describing the phenomenon.
1. EXPERIMENT
The theoretical investigation was preceded by the
experiments on inducing the HF oscillations in a NLTL
partially filled with ferrite, which is in a state close to
full magnetization [6].
Fig. 1. Schematics of the analyzed system
Fig. 2. The experimental results
The 200VNP-type NiZn ferrite was selected as the
nonlinear material, which according to [2], provided the
best results on formation the HF oscillations. The ana-
lyzed system (Fig. 1) consisted of the following ele-
ments: (i) two matching coaxial lines, TL1 and TL2,
filled with a liquid dielectric (ε=2.25,
D3/D1=26 mm/12 mm), and (ii) coaxial NLTL (D3/D1 =
26 mm/12mm, length l = 850 mm), including the coaxi-
al layers of ferrite (ε= 10, D2/D1 = 20 mm/12 mm), and
liquid dielectric (ε= 2.25, D3/D2 = 26 mm/20 mm).
At H0=110 kA/m and U0=100 kV the HF oscilla-
tions with the frequency of 1.58 GHz and amplitude
efficiency up to 27% were obtained (Fig. 2).
2. 1D MODEL
The analyzed system (Fig. 1) can be represented
most simply in the form of a 1D model described else-
where earlier [2, 3]. In this case, the propagation of the
current impulse and related electromagnetic wave along
the transmission line with a magnetic nonlinearity is
described by telegraph equations [1, 2], which can be
reduced to a second order equation for the current I:
( )22
2 2
1 ,
I K MI C I ILC RC
z t C z z t
ϕ∂ + ⋅∂ ∂ ∂ ∂
= + −
∂ ∂ ∂ ∂ ∂
(1)
where C and R are the specific capacitance and re-
sistance of the line, L is the specific inductance of the
line without regard to magnetic properties, K = μ0(D2-
D1)/2l, μ0 is the magnetic permeability of the vacuum,
Mφ is the azimuthal component of the magnetization,
D2, D1 and l are the external and internal diameters and
length of the ferrite.
The external longitudinal magnetic field Н0 turns the
ferrite in a saturated state with the magnetization Ms. In
these circumstances, the individual electron spins be-
have as single units, participating in creation of a com-
mon axial magnetic flux. The state of the ferrite dynam-
ics can be described by one variable – the magnetic
moment vector M, while the azimuthal magnetic field of
the high voltage impulse does not change its amplitude,
but the direction only, |M|=Ms=const. The vector M
dynamics dependent on the magnetic field H is de-
scribed by Landau-Lifshitz equation
[ ] [ ]0
0
s
d
dt M
γµγµ α = × − × ×
M M H M M H , (2)
where γ is the electron gyromagnetic ratio, and α is the
phenomenological relaxation factor.
The vector of the magnetization has the form
mailto:magda@kipt.kharkov.ua
ISSN 1562-6016. ВАНТ. 2015. №6(100) 69
z
M
M
M
ρ
ϕ
=
M
,
and the initial states of its components are: Mρ=Mφ=0,
Mz=Ms. The magnetization moment at saturation Ms
depends on properties of used ferrite.
The magnetic field vector H has the components:
Hρ=(Hdm)ρ , Hφ=qI, Hz=H0+(Hdm)z. Here qI is the azi-
muthal magnetic field of the high voltage pulse, where
the form-factor q, according to [3] and assuming the
absence of layered structure of the NLTL is defined as
follows
1
eff
q dπ= , where ( ) 2
2 1
1
/ lneff
Dd D D
D
= − . In this case,
the radial effective magnetic field
(Hdm)ρ= -Mρ, (3)
depends on the ferrite shape, while the axial magnetic
field with the magnetizing factor
(Hdm)z=-k(Mz-Ms), (4)
takes into account the magnetic field of the solenoidal
currents induced in the walls of the waveguide [1, 3] by
means of the coupling coefficient 0<k<1.
A method of numerical calculation of the presented
model is proposed in [2], which is based on splitting the
transmission line into a number of sections, with insert-
ed voltage sources which correspond to the contribution
of the magnetic subsystem (2). Unlike [2], this study
presents a direct integration of the telegraph equation
(1) together with equation (2) by the Runge-Kutta
method. In addition, the present case takes into account
not only the line with ferrite, but the matching lines TL1
and TL2 also. This allows to estimating the matching
effects between the lines.
Thus, for combined solution of the equations (1) and
(2) a grid is formed with the dimensions n×N, where
n=l/Δz, N=T/Δt, N is the calculation time, Δz and Δt are
the lengths of discretization steps in space and time,
respectively. Each cell of the grid is associated with a
current of value Ii,j and magnetic moment Mi,j with
three components, (Mρ)i,j, (Mφi,j and (Mz)i,j, i=1,2,...n,
j=1,2...N.
At each solution step the computation is performed
in three stages:
(i) determining the net value of IS=I i+1,j+K⋅(Mφ)i+1,j
(whose individual components are not known yet) for
the next step, through numerical solution of the tele-
graph equation (1) by the finite difference method;
(ii) determining the magnetic moment for the next
time-step by means of numerical solution of the Lan-
dau-Lifshitz equation (2) by the Runge-Kutta method;
(iii) determining the current for the next time-step
Ii+1,j=IS-K⋅(Mφ)i+1,j.
The results of numerical simulation are shown in
Figs. 3 and 4. Fig. 3 demonstrates an increase of the
oscillation frequency with the input voltage, and de-
crease with the longitudinal magnetizing field. This is in
agreement with the experimental data [2], suggesting a
qualitative correctness of the 1D model in describing the
phenomenon under investigation. At the same time, the
oscillation frequency obtained in the numerical experi-
ment, which ignores the layered structure of the system,
is substantially higher than in [2] and in our experiments
[6] (see Fig. 4).
Fig. 3. 1D model: dependence of the oscillation
frequency (1), and amplitude (2) on the input voltage
for H0=100 kA/m (a), and on the longitudinal
magnetizing field for Hφ=110 kA/m (b)
Fig. 4. Comparison of the output signals obtained
in the experiment, and in 1D (a) and 2D (b) simulations
3. 2D MODEL
To create a 2D model of the system, the full set of
Maxwell’s equations for a cylindrical coordinate system
(z,ρ,φ) is used: z is the distance along the coaxial struc-
ture, ρ is the distance from the axis of symmetry of the
system, φ is the azimuthal angle with respect to the axis
of symmetry. Due to homogeneity of the system and
homogeneity of the initial and boundary conditions on
angle φ) (the system is excited by a TEM wave), it can
be accepted d/dφ)≡ 0, thus going over to a two-
dimensional model. Then the set of Maxwell equations
splits into two independent sets,
( )
( ) ( )
( )
0
0
0
1 ;
1 1 ;
.
z
z
E H
t z
HE
t
H M EE
t z
ρ φ
φ
φ φ ρ
∂ ε ∂
⋅ = −
η ∂ ∂
∂ ρ∂ ε ⋅ = η ∂ ρ ∂ρ
∂ + ∂∂η = − ∂ ∂ρ ∂
(5)
ISSN 1562-6016. ВАНТ. 2015. №6(100) 70
( )
( ) ( )
( )
0
0
0
;
1 ;
1 ,
z z
z
H M E
t z
EH M
t
E H H
t z
ρ ρ φ
φ
φ ρ
∂ + ∂η =
∂ ∂
∂ ρ∂ +η = − ∂ ρ ∂ρ
∂ ε ∂ ∂ ⋅ = −η ∂ ∂ ∂ρ
(6)
where η0 is the free space impedance.
Fig. 5. 2D model: dependence of the oscillation fre-
quency (1) and amplitude span (2) on the input voltage,
for H0=100 kA/m (a), and the longitudinal bias magnet-
ic field for Hφ=110 kA/m (b)
Fig. 6. Dependences of (a) the output waveform,
and (b) of the oscillation frequency (1) and amplitude
(2) on the outer diameter of the NLTL
The system of equations (5) describes a TE wave
that is more general case of a TEM wave propagating in
the coaxial structure. The equation set (6) describes a
TM wave, which is not formed in the coaxial structure
when it is excited by a TEM wave. But in the investi-
gated system the TM wave can be formed as a result of
interaction with the magnetic sub-system governed by
equation (2). The numerical calculation of equations (5)
and (6) is carried out in accordance with the methods
established in [7], while with regard to the interaction
between the electromagnetic fields and magnetic sub-
system (2) we use the method described in the previous
section. The results of numerical simulation are shown
in Figs. 5 and 6. As can be seen, when 2D modeling is
used the shape of the output impulse corresponds better
to the experimental waveform than in the case of 1D
modeling. In particular, the oscillation frequency ob-
tained in the 2D model (2.05 GHz) is much closer to the
experimental result (1.6 GHz) than to the 1D one (8.5
GHz).
4. DISCUSSION OF THE RESULTS
Based on the described 2D numerical study, several
issues of practical interest can be considered.
(i) Optimizing the filling factor of a coaxial NLTL
with ferrite. To study this effect, a series of numerical
experiments with various outer diameters D3 of the sys-
tem (see Fig. 1) were produced. Fig. 6 indicates the ex-
istence of a maximum oscillation amplitude for a certain
D3. In our case, it is observed for D3=28 mm, corre-
sponding to the filling factor of the ferrite in the wave-
guide cross-section equal to 0.4. It is significant that
when the filling factor is close to unity the oscillation
frequency goes high and corresponds roughly to the
results of the 1D model. However when the filling fac-
tor decreases the oscillation frequency also rapidly de-
creases. This suggests that the frequency of HF oscilla-
tions in a multilayered structure of the NLTL depends
on the transverse distribution of the electromagnetic
field that cannot be considered in a 1D model.
(ii) The NLTL transverse dimensions. To increase
the power of HF oscillations the input voltage U0
should be increased. Respectively, to provide a higher
electrical strength it is necessary to increase the cross-
section of the coaxial system. However, increasing the
transverse dimensions necessarily leads to dominance of
the effects specific for the layered waveguide structure,
associated with the transformation of TEM wave, and,
as the result, distortion of the output pulse. To explore
this issue, a series of numerical experiments with a pro-
portional variation of the input voltage U=sU0 and
transverse dimensions of the system Di=sDi
0, where s is
a variable scale factor. Fig. 7,a presents a series of the
output waveforms, obtained for the excitation signal of
the amplitude U0 = 100 kV and pulse width at half max-
imum tp0.5 = 6 ns. It can be seen, the reduced span ΔU/s
of the oscillation amplitude increases when s goes up to
the value 3, i.e. the oscillation excitation efficiency aris-
es.
It should be noted that the growth of s reduces the
oscillation frequency (an effect that is absent in the 1D
model) as well as the number of the observed oscillation
periods since the current pulse width is limited. In fact,
ISSN 1562-6016. ВАНТ. 2015. №6(100) 71
since s=3 (for tp 0.5 = 6 ns) the oscillations practically
cease, such that no more than 1or 2 periods can be ob-
served (see Fig. 7). With greater widths of the current
impulse the oscillations are observed at lower frequen-
cies.
Fig. 7. The output impulse envelope vs s (a).
Dependence of the oscillation frequency (1) and
reduced amplitude span (2) on the scale factor s (b)
Fig. 8. Dependence of the oscillation frequency (1),
and amplitude span (2) on the insulation (a)
and ferrite (b) permittivity
(iii) The effect of dielectric characteristics of the
NLTL media on the excitation efficiency of oscillations.
A series of numerical experiments with variation of the
permittivity of the liquid dielectric εd and ferrite materi-
al εf were performed. These results are shown in Fig. 8.
As can be seen, when εf decreases and εd increases, the
oscillation frequency goes up, while the oscillation am-
plitude decreases. Thus, to provide for an efficient for-
mation of HF oscillations the permittivity of the ferrite
should significantly exceed the value of the permittivity
of the insulating dielectric.
By way of example, for a coaxial NLTL with di-
mensions D3/D1 = 2.2, excited by an input pulse of
amplitude 100 kV and a 6 ns width the following condi-
tions for effective excitation of oscillations can be ob-
tained:
- the factor of filling the line’s cross-section with the
ferrite material should be about 0.4;
- the permittivity of an insulating dielectric should
be at least three times lower than the permittivity of the
ferrite, εf > 3εd.
CONCLUSIONS
A 2D simulation model has been used for the first
time to describe the dynamics of the shock wave and the
HF oscillations excited by a current impulse traveling
along the nonlinear coaxial line partially filled with a
longitudinally magnetized ferrite. The 2D model has
major advantages over the 1D model and agrees much
better with experimental results. The computations
based on the 2D model allow formulating conditions for
an effective formation of HF oscillations in the NLTL.
ACKNOWLEDGEMENT
The authors are grateful to Dr. V. Pazynin for con-
sultations on the numerical technique for solving the
Maxwell equations.
REFERENCES
1. I.G. Katayev. Electromagnetic shock waves. Lon-
don: Iliffe Books Ltd, 1966, 152 p.
2. J.E. Dolan. J. Phys. Simulation of shock waves in
ferrite-loaded coaxial transmission lines with axial
bias // D: Appl. Phys. 1999, v. 32, p. 1826-1831.
3. J.W.B. Bragg, J. Dickens, A. Neuber, K. Long //
Proc. of 2011 COMSOL Conf. Boston, Burlington,
MA, Feb. 2011.
4. V.P. Gubanov, A.V. Gunin, O.B. Kowalchuk, et al.
Efficient conversion of the energy of high-voltage
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transmission line with a saturated ferrite // Pisma
ZhTF. 2009, v. 35, issue 13, p. 81-87 (in Russian).
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magnetic Nonlinear Transmission Lines as Compact
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electrical engineering. Texas Tech University, Dec.
2013, 81 p.
6. S.Y. Karelin, V.B. Krasovitsky, I.I. Magda, V.S. Mukhin,
and V.G. Sinitsin. An experimental study of quasi-
monochromatic oscillations in a ferrite-filled trans-
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2000, 852 p.
Article received 20.10.2015
ISSN 1562-6016. ВАНТ. 2015. №6(100) 72
ВОЗБУЖДЕНИЕ ВЫСОКОЧАСТОТНЫХ ОСЦИЛЛЯЦИЙ В КОАКСИАЛЬНОЙ ЛИНИИ
С НАМАГНИЧЕННЫМ ФЕРРИТОМ. 2D-МОДЕЛЬ
Ч.В. Ан, С.Ю. Карелин, В.Б. Красовицкий, Х.О. Куон, И.И. Магда, В.С. Мухин, В.Г. Синицын
Представлена методика и результаты 1D- и 2D-численного моделирования процесса формирования вы-
сокочастотных колебаний в коаксиальной нелинейной линии, частично заполненной ферритом, который
намагничен продольным магнитным полем. С помощью 2D-модели впервые исследованы динамика и
структура волнового поля нелинейной линии с поперечной неоднородностью. Обсуждается оптимизация
диэлектрических параметров системы, размеров линии и степени ее заполнения ферримагнитным материа-
лом, необходимых для повышения электрической прочности и получения максимальной интенсивности ко-
лебаний.
ЗБУДЖЕННЯ ВИСОКОЧАСТОТНИХ ОСЦИЛЯЦІЙ В КОАКСІАЛЬНІЙ ЛІНІЇ
З НАМАГНІЧЕНИМ ФЕРИТОМ. 2D-МОДЕЛЬ
Ч.В. Ан, С.Ю. Карелін, В.Б. Красовицький, Х.О. Куон, І.І. Магда, В.С. Мухін, В.Г. Сініцин
Представлено методику та результати 1D- і 2D-чисельного моделювання процесу формування високоча-
стотних коливань у коаксіальній нелінійній лінії, що частково заповнена феритом, який намагнічено повздо-
вжнім магнітним полем. За допомогою 2D-моделі вперше досліджено динаміку та структуру хвильового
поля нелінійної лінії з поперечною неоднорідністю. Обговорюється оптимізація діелектричних параметрів
системи, розмірів лінії та ступеня її заповнення феромагнітним матеріалом, які необхідні для підвищення
електричної стійкості та отримання максимальної інтенсивності коливань.
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