Field analysis of a dielectric-loaded rectangular waveguide accelerating structure. Page: 2 of 3
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A ky cos-(x+-)cosky,,y,0<y<a
E = W 2
B1 kIW cos- 2(x+-)sinnk'(b-y),a<y<b
w w 2
AEkk= sin w(x+-)sinky")y,0<y<a
Bk,,kk, sin-(x+-)cosk'>)(b- y),a < y <b
A,,(-j,,,)k( m sin (x+r)cosk( )y,0<y<a
w 2 (3)
B,,(-j,,,)k>, sin - (x+-)sink) (b-y),a<y<b
Tr- ,o, sin -(x+ -)sin k 0 y,0 <y< a
H = W 2
-B,,CoEoe,/3, sin (x+-)cosk) ,(b-y),a<y<b
mA mA 2
A, (jwE0)-cos-(x+-)sink y,0 <y <a
H w w 2
Bi (JWEEr) cos W(x+ )cosk 21(b- y),a < y <b
Lw w 2
where kemn2=(m-/w)2+-mn2. Note that exp(-j-mnz) has
been omitted in these expressions for simplicity.
At the interface between the region 0 and I, the
tangential electric and magnetic field components are
Ak cos k a = B1 k' sin k"' (b - a), (4a)
A_ sin k0 a = B_ e, cos k0 (b - a), (4b)
Dividing (4a) by (4b) yields the dispersion relation,
kt', tan(ky21,(b - a))= Ek0 cot(k20) a) (5)
This is a transcendental equation of the general form
of a complex function of Jlmn and f For the
inhomogeneous guide considered here, the dispersion
relation must be solved numerically. An infinite
number of discrete solutions exist.
From (4), the coefficient ratio A/B can be found,
and, when substituted into (3), completes the solution.
3. PROPERTIES OF THE LSM , AS
In general, the relative advantages of accelerating
structures can be understood with reference to figures
of merit such as the ratio of the peak surface electric
field to the axial acceleration field E/EO, the group
velocity vg, the attenuation constant *, and R/Q which
measures the efficiency of acceleration in terms of the
given stored energy, etc. The definitions of these
parameters will be quantified here. In this section,
only the results pertaining to the LSM11 mode are
given, because the LSM11 mode is the lowest luminal
mode in our considered structures. And also because
its symmetrical field distribution in x and y-direction.
3.1 The ratio of surface field E, to accelerating field Eo
E, E,(0,b) + + w
E E 0,0) k sin k a = sin( a)
E E, ky/
It is desirable to have this ratio as small as possible
since the surface field contributes nothing to
accelerating the beam but is responsible for breakdown
of the structure.
3.2 The group velocity vg
v =- P=-JJE H dxdy
g U 2
2L ( 0 r (y)(E2 +Ey +E2)+p0(H2 +Hz ))dxdydz
where P is the power flow over the half section under
consideration and U is the stored energy per unit length
in the half structure.
3.3 The quality factor Q (ignoring dielectric losses)
and the attenuation constant-
P,, = R, sf ds
R = and 5s, 2
S* a- p ao
where - is the conductivity of the metal wall.
a loss (9)
3.4 The normalised shunt impedance R/Q
R E v
ep" (10 )
where Eo is the maximum accelerating field on the z-
4. NUMERICAL RESULTS
Figure 2 shows the dispersion curves of the lower
LSMm1 and LSEm, modes for an X-band structure.
Because the LSM11 mode is the lowest luminal mode
and its field distribution pattern, it will be chosen as the
accelerating mode. Figure 3 gives the normalized
longitudinal electric field distributions of the LSM
synchronous mode as a function of x and y using the
field analysis method.
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Xiao, L.; Gai, W. & Sun, X. Field analysis of a dielectric-loaded rectangular waveguide accelerating structure., article, July 16, 2001; Illinois. (digital.library.unt.edu/ark:/67531/metadc723231/m1/2/: accessed December 13, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.