The thin structure of waveguide dielectric accelerating system elements
Last years the works appeared in which models of artificial dielectrics containing in a frequency band simultaneously negative values of the dielectric permittivity and magnetic permeability were discussed [1, 2]. As is shown in [3], the electromagnetic wave propagation in such a media is characteri...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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irk-123456789-790052015-03-25T03:01:49Z The thin structure of waveguide dielectric accelerating system elements Bryzgalov, G.A. Nikolaichuk, L.N. Khizhnyak, N.A. Last years the works appeared in which models of artificial dielectrics containing in a frequency band simultaneously negative values of the dielectric permittivity and magnetic permeability were discussed [1, 2]. As is shown in [3], the electromagnetic wave propagation in such a media is characterized with peculiarities that are important to understand the electromagnetic radiation interaction with tissues in vivo. The aim of this work is to show that such a media in organic nature can be meet at every step, and the mechanism of formation of simultaneous negative values of ε(ω) and μ(ω) is contained already by their physical structures. Moreover, experimental facts are known confirming the existence of positive and negative values of ε and μ in a narrow frequency band that, unfortunately, is still not completely understood till now. 2001 Article The thin structure of waveguide dielectric accelerating system elements / G.A. Bryzgalov, L.N. Nikolaichuk, N.A. Khizhnyak // Вопросы атомной науки и техники. — 2001. — № 5. — С. 150-153. — Бібліогр.: 13 назв. — англ. 1562-6016 PACS number: 29.17.+w http://dspace.nbuv.gov.ua/handle/123456789/79005 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Last years the works appeared in which models of artificial dielectrics containing in a frequency band simultaneously negative values of the dielectric permittivity and magnetic permeability were discussed [1, 2]. As is shown in [3], the electromagnetic wave propagation in such a media is characterized with peculiarities that are important to understand the electromagnetic radiation interaction with tissues in vivo.
The aim of this work is to show that such a media in organic nature can be meet at every step, and the mechanism of formation of simultaneous negative values of ε(ω) and μ(ω) is contained already by their physical structures. Moreover, experimental facts are known confirming the existence of positive and negative values of ε and μ in a narrow frequency band that, unfortunately, is still not completely understood till now. |
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Article |
| author |
Bryzgalov, G.A. Nikolaichuk, L.N. Khizhnyak, N.A. |
| spellingShingle |
Bryzgalov, G.A. Nikolaichuk, L.N. Khizhnyak, N.A. The thin structure of waveguide dielectric accelerating system elements Вопросы атомной науки и техники |
| author_facet |
Bryzgalov, G.A. Nikolaichuk, L.N. Khizhnyak, N.A. |
| author_sort |
Bryzgalov, G.A. |
| title |
The thin structure of waveguide dielectric accelerating system elements |
| title_short |
The thin structure of waveguide dielectric accelerating system elements |
| title_full |
The thin structure of waveguide dielectric accelerating system elements |
| title_fullStr |
The thin structure of waveguide dielectric accelerating system elements |
| title_full_unstemmed |
The thin structure of waveguide dielectric accelerating system elements |
| title_sort |
thin structure of waveguide dielectric accelerating system elements |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2001 |
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http://dspace.nbuv.gov.ua/handle/123456789/79005 |
| citation_txt |
The thin structure of waveguide dielectric accelerating system elements / G.A. Bryzgalov, L.N. Nikolaichuk, N.A. Khizhnyak // Вопросы атомной науки и техники. — 2001. — № 5. — С. 150-153. — Бібліогр.: 13 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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THE THIN STRUCTURE OF WAVEGUIDE DIELECTRIC
ACCELERATING SYSTEM ELEMENTS
G.A. Bryzgalov, L.N. Nikolaichuk, N.A. Khizhnyak
National Seintific Center, Kharkov Institute of Physics and Technology,
Akademicheskaya, 1, 61108, Kharkov, Ukraine
E-mail: bryzgalov@kipt.kharkov.ua
Last years the works appeared in which models of artificial dielectrics containing in a frequency band simultaneous-
ly negative values of the dielectric permittivity and magnetic permeability were discussed [1, 2]. As is shown in [3],
the electromagnetic wave propagation in such a media is characterized with peculiarities that are important to under-
stand the electromagnetic radiation interaction with tissues in vivo.
The aim of this work is to show that such a media in organic nature can be meet at every step, and the mechanism of
formation of simultaneous negative values of ( )ωε and ( )ωµ is contained already by their physical structures.
Moreover, experimental facts are known confirming the existence of positive and negative values of ε and µ in a
narrow frequency band that, unfortunately, is still not completely understood till now.
PACS number: 29.17.+w
1 RESONANCE SCATTERING OF ELEC-
TROMAGNETIC WAVES ON THE DIELEC-
TRIC SPHERE
The problem of electromagnetic wave scattering on
the homogeneous dielectric sphere was solved yet at the
beginning of the ХХ-th century [4, 5], but we should
use this problem solution in the shape of [6] to investi-
gate the problem of our interest by analytical methods.
If the center of a sphere is placed at the origin of coordi-
nates and its radius is denoted with a then for the inci-
dent plane linearly polarized electromagnetic wave we
have
( ) rkieErE
1
0
−= (1)
(the time dependence tie ω is omitted), where
( )01011 ,0, θθ CoskSinkk =
(2)
and the vector of the electric field intensity 0E
forms
the angle β with the plane zx0 . Here
111 µεω
c
k = , where 1ε and 1µ are the dielectric
permittivity and magnetic permeability of the environ-
ment, 0θ is the angle between the vector 1k
and the
axis z0 .
The scattering field in a wave band has the shape [
7, 8]
( ) ( ) ( ) ( )[ ] ( ) ( ) ( )[ ]{ }∑ ∑
∞
=
+
−=
⊥
−
−−+−−=
1
0
,,
0
,||,
1
1
J
J
Jm
mJmJ
rikr
расс emSinAemCosA
rk
eirE ϕθ βϕθβϕθ
(3)
( ) ( ) ( ) ( )[ ] ( ) ( ) ( )[ ]{ }∑ ∑
∞
= −=
⊥
−
−+−−=
1
0
,||,
0
,,
1
1
1
J
J
Jm
mJmJ
rik
расс emCosAemSinA
rk
ierH ϕθ βϕθβϕθ
µ
ε
(4)
Here
( ) ( ) ( ) ( ) ( )
( ) ( )
( ) ( ) ( ) ( )
++
++
−+−= +
+
θ
θ
θθ
ε
µθ
µ
µ
d
CosdP
BCosPCosecmB
J
J
mJJJ
mJJA J
mJJJmJJ
mJ
mJ
0
,,
0
,1,
1
10
,||,
12
!1
!121 (5)
( ) ( ) ( ) ( )( )
( )( )
( ) ( )
( ) ( ) ]θθ
θ
θ
ε
µθ
µ
µ
CosPmCosecB
d
CosdPB
J
J
mJJJ
mJJA
JmJJ
J
mJJ
mJ
mJ
0
,,
0
,1,
1
10
,,
12
!1
!121
+
+
+
++
−+−−= +
+
⊥
(6)
are the amplitudes of a scattering wave representing for
further investigations the basic interest. Notice that con-
stants ( )0
,1, mJJB + and ( )0
,, mJJB in their turn have parame-
ters of the scattering sphere and equal
( ) ( ) ( )
( ) ( ) jmJJ QmCosec
mJJJ
mJJiB 0
1
10
,, !1
!12 θ
µ
ε
++
−++= (7)
( ) ( )
( ) ( )
( )
J
J
mJJ P
d
CosdP
mJJJ
mJJiB
θ
θ
µ
ε µ
!1
!
1
10
,1, ++
−−=+ (8)
( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )1
2
2
1
1
1
2
2
12
1
1
12
χχ
µ ε
εµχχ
χχ
µ ε
εµχχ
′−′
′−′
=
JJJJ
JJJJ
j
hjhj
jjjj
Q (9)
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.
Серия: Ядерно-физические исследования (39), с. 150-153.
150
( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )1
2
21
2
2
1
1
1212
1
1
χχχχ
µ ε
εµ
χχχχ
µ ε
εµ
JJJJ
JJJJ
j
hjhj
jjjj
P
−′
′−′
= (10)
where ka111 µεχ = , kaε µχ =2 , ( )xjJ and
( ) ( )xhJ
2 are the spherical radial functions of order J ,
expressed in terms of the cylindrical Bessel’s and
Henkel’s functions of the half whole index by relations
( ) ( )xJ
x
xj JJ
2
12 +
= π
, ( ) ( ) ( ) ( )xH
x
xh JJ
2
2
1
2
2 +
= π
, (11)
Here ε and µ are the dielectric permittivity and mag-
netic permeability of the material of the scattering and
dielectric sphere manufactured. Multipliers jQ and jP
have bands on the plane of the complex variable ω ,
these bands referring to resonance properties of the di-
electric sphere corresponding to the dispersion equa-
tions were also discussed in literature and nevertheless a
number of properties of these equations were not yet
studied completely. Note only the denominator of the
value of jQ , expressed by Bessel′s cylindrical func-
tions (11) is written as
( )
( )
( ) ( )
( ) ( )
−=−
+
−
+
−
111
2
2
1
1
2
2
1
1
1
2
2
1
2
2
1
1
ε
ε
χχ
χ
µ ε
εµ
χ
χ J
H
H
J
J
J
J
J
J
, (12)
and the denominator of the value of jP of the same
functions has the shape
( )
( )
( ) ( )
( ) ( )
−=−
+
−
+
−
111
2
2
1
1
2
2
1
1
1
2
2
1
2
2
1
1
µ
µ
χχ
χ
ε µ
µε
χ
χ J
H
H
J
J
J
J
J
J
(13)
Equation (12) is the dispersion equation of TH modes of
dielectric sphere oscillations from which 0=pH , and
equation (13) is the dispersion equation of TE mode os-
cillations of the dielectric sphere, respectively, where
0=pE . These equations were investigated by numeri-
cal methods in [9].
2 THE AMPLITUDE OF ELECTROMAG-
NETIC WAVE SCATTERING ON A SMALL
DIELECTRIC SPHERE WITH HIGH PER-
MITTIVITY
If the sphere radius is small 11 < <χ , then using
the Bessel′s function asymptotic for small argument val-
ues we find that 12
1
+≅ J
jQ χ and 12
1
+≅ J
jP χ . Con-
sequently, for small 1χ only the first items with 1=J
play the essential role (3,4). Taking notice, that Bessel′s
cylindrical functions with a half whole index J are re-
duced to the trigonometric functions and therefore in
case of the small 1χ and arbitrary 2χ we find
( )
( ) ( ) ( )
( ) 222
2
2
222
2
1
1
222
2
2
222
1
222
2
2
222
1
3
1
1
1
1
1
1
1
21
3
χχχχ
χχχχχ
χχχχ
χχχ
ε
ε
χχχχ
χχχ
ε
ε
χ
CosSin
CosSinii
CosSin
CosSin
CosSin
CosSin
iQ
+−
−
+−
+−
−
+
+−
−
−
= (14)
The value of 1χ in the denominator has been con-
served for that the denominator be not converted to zero
for any 2χ . If one supposes that in the denominator the
items with 1χ are negligibly small in comparison with
the other items then one can write
1'
1'
3
1
1 23
2
εε
εεχ
+
−
=
eff
effiQ (15)
where
( )2χεε Feff = (16)
and
( ) ( ) 222
2
2
222
2 1
2
χχχχ
χχχχ
CosSin
CosSinF
+−
−= (17)
and finally, if 12 < <χ , then ( ) 12 →χF and
1
1
3
1
1 23
2
εε
εεχ
+
−−= iQ (18)
This expression coincides with that of the dipole
moment of the dielectric sphere obtained in the long
wave approximation. Therefore by analogy with the
above approximation one can suppose that the dielectric
sphere with a high value of dielectrical permittivity and
in any frequency range with respect to electrodynamics
is equivalent to the sphere manufactured from dielec-
trics the effective permittivities of which are equal (16).
In the approximation 11 < <χ the value of jP per-
mits the essential simplification. Really then it has a
sense to consider only the item with 1=J :
( )
( ) ( ) ( )
( ) 222
2
2
222
2
1
1
222
2
2
222
1
222
2
2
222
1
3
1
1
1
1
1
1
1
21
3
χχχχ
χχχχχ
χχχχ
χχχ
µ
µ
χχχχ
χχχ
µ
µ
χ
CosSin
CosSinii
CosSin
CosSin
CosSin
CosSin
iP
+−
−
+−
+−
−
+
+−
−
−
= (19)
In case of 21 χχ < < we find that
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.
Серия: Ядерно-физические исследования (39), с. 151-153.
151
2
1
3
2 3
11 +
−
−=
eff
effiP
µ
µ
χ (20)
where
( )2χµµ Feff = (21)
The function ( )2χF in this case turns to the same
one as for the introduction of the effective value of per-
mittivity effε (17).
In the limiting case 11 < <χ and 12 < <χ , we
find
1
13
11 23
2
µµ
µµχ
+
−−= iP (22)
that coincides with the magnetic dipole moment ob-
tained for the magnetic sphere. It permits to suppose
that in the high-frequency region when ( )2χF can ac-
cept both positive and negative values of 1Q and 1P ,
despite on the smallness the parameter 1χ can be high
due to the smallness of denominators
02 1 →+ εε eff (23)
02 1 →+ µµ eff (24)
The condition (23) determines the condition of aris-
ing the electrical resonance and the condition (24) –
refers to the magnetic one of the sphere.
0 1 2 3 4 5 6 7 8 9 10
-2
0
2
4
x
F(
x)
Fig. 1. The graph of the function ( )χF . The points
refer to resonances of the dielectric sphere:
- magnetic resonances, ( ) 2−=χF ;
- electrical resonances, ( )
ε
ε
χ 12
−=F ;
- electrical resonances of passing, ( )
ε
εχ 1=F ;
- magnetic resonances of passing, ( ) 1=χF .
Thus resonance conditions depend essentially on ge-
ometric sphere dimensions then resonances themselves
were called as geometric ones.
The graph of the function ( )χF is shown in Fig. 1
and it shows effective values of the dielectric permittivi-
ty and magnetic permeability of the sphere material and
above mentioned graph was firstly defined in [10], and
by rigorous electrodynamical calculations in [7, 8].
3 THE EXPERIMENTAL INVESTIGATION
OF ELECTROMAGNETIC WAVE SCAT-
TERING ON DIELECTRIC SPHERES WITH
HIGH VALUES OF THE DIELECTRIC PER-
MITTIVITY
In the process of manufacturin articles from titanium
dioxide (natural ТiО2, crystal grinding, mixing, and suc-
cessive fabrication from this mixture and a binder of ar-
ticles) it was necessary to control the quality of isotropic
dielectrics made on their basis. For this aim probes,
from which one fabricated specimens of a spherical
form, were taken from different places of the mix and
resonance properties were studied in the 10-sm range of
wavelengths. Resonance frequencies were calculated ac-
cording to relations (16) and (21) and compared with
experimental measurements [11, 12].
Fig. 2. The graph of the dependence of the reflection
factor on the frequency of the dielectric sphere from
TiO2, with 13.20 mm in diameter placed in the cen-
ter of the rectangular waveguide.
Typical experimental curves are shown in Fig. 2 for
magnetic and dielectric oscillations in the dielectric
sphere. In case of electrical oscillations the resonance
curves are similar to magnetic ones but the minimum is
on the left of the maximum of the reflection factor.
The position of resonance was used to precise mea-
surements of high values of ε in a wide range of fre-
quencies and temperatures. However in these experi-
ments resonance splitting even for spheres of a small ra-
dius and the position minimum values of the reflection
factor have not been explained. These peculiarities be-
come obvious if to take account that for definite values
of ( )χF ε and µ are negative. Indeed in these cases
the electrical dipole moment of a sphere (15) refers to
the wave reflection factor and behaves itself as in
(Fig. 1). Therefore under conditions of resonance (23)
the dipole momentum passes through zero in the nega-
tive part that reduces to the maximum splitting shown in
Fig. 2 (η is dependent on the dipole momentum modu-
lus).
Further the dipole momentum has its turn again to
the region of positive values and when it is zero the re-
flection factor is again zero. On the graph of Fig. 1 char-
152
acteristic points of the reflection factor value are shown
for ( )χF as a function of frequency. Black points
show the position of magnetic resonances and values for
which the minimum is defined and light points relate to
the position of electrical resonance’s in the region of
negative ( )χF and the position of minima of reflec-
tions for positive values of ( )χF .
Fig. 3. Transfer ratio versus the frequency of a sin-
gle dielectric disc from TiO2 of the thickness of
3.291 mm, with the central hole of 5 mm in diameter
in a circular half endless waveguide of 81.5 mm in
inner diameter Е01 oscillations have been excited.
The analogous relation is observed for more massive
dielectric specimens. In the graph of Fig. 3 the depen-
dence of the gain factor is presented (the value opposite
to the reflection factor) for the dielectric disc overlap-
ping the section of a circular waveguide. As in case of a
sphere a signal has a minimum determining wave pass-
ing and then transition of the dielectric permittivity of
the disk as a whole one to the negative region in the
place of maximum splitting (on modulus). This value
refers to positive ones and after deviation from the reso-
nance value turns to the average value.
The value of effε is defined according to the fre-
quency of resonance curve splitting. This value of effε
was used to calculate the waveguide dielectric reso-
nance accelerating structure on the basis of the circular
waveguide loaded by dielectric discs and was confirmed
experimentally [12, 13].
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ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.
Серия: Ядерно-физические исследования (39), с. 153-153.
153
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