t t t t n n n n E E H H D D B B  

t t t t n n n n E E H H D D B B    
       
(4)
(c) Absorbing boundary condition. At both ends of the rectangular
wave guide, the first-order absorbing conditions are applied:
y y E E
t z

 

 
 
(5)
The symbol ± represents forward or backward waves, andυis the
phase velocity of the microwave (m/s).
(d) Oscillation of the electric and magnetic field intensities by
magnetron. The incident wave due to the magnetron is given by the
following equations:
    ,
yin
y yin x
x H x
E πx πx
E =E sin sin 2πft H = sin sin 2πft
L Z L
   
   
   
(6)
Z
H
is the wave impedance defined as:
g I g 0
H
0 0 0
λZ λ μ
Z = =
λ λ ε
(7)
Fig. 2. The electromagnetic field distribution on x-zplane and
a physical model.
Thefinite difference time domain method was applied to predict the
electric and magnetic fields; the leapfrog scheme was implemented
using Maxwell’s equations. The electric field vector components were
offset one half cell in the direction of their corresponding components,
while the magnetic field vector components were offset one half cell in
each direction orthogonal to their corresponding components. The
electric and magnetic fields were both evaluated at every other half-time
step. For the TE
10
mode, the electric field and magnetic field
components are expressed with the total field FDTD equations thus:
 
 
1/ 2 1/ 2
1
1/ 2 1/ 2
(, )
1
( 1/ 2, ) ( 1/ 2, ) 1 2( , )
( , ) ( , )
( , ) ( , ) ( , )
1 1
2 ( , ) 2 ( , )
( , 1/ 2) ( , 1/ 2)
n n
z z
n n
y y
n n
x x
i k t
H i k H i k t i k
E i k E i k
i k t i k t i k x
i k i k
H i k H i k
z
 

 
 

      
   
     
   
 
    



1/2 1/2
(, 1) ( , )
(, 1/2) ( , 1/2)
( , 1/2)
n n
y y n n
x x
E i k E i k t
H i k H i k
i k z
 
      
     
      
1/ 2 1/ 2
( 1, ) ( , )
( 1 / 2, ) ( 1 / 2, )
( 1/ 2, )
n n
y y n n
z z
E i k E i k t
H i k H i k
i k x
 
      
     
      
…(8)