Optimizing the Parameters of a 12-Cavity Rising-Sun Relativistic Magnetron With Single-Stepped Cavities for $\pi $ -Mode Operation

We investigated the use of single-stepped cavities instead of typical tapered cavities in an A6 magnetron with diffraction output (MDO) and a 12-cavity MDO through particle-in-cell (PIC) simulations using MAGIC
[1]
and UNIPIC
[2]
in our earlier publications
[3]
–

[5]
. The interaction space, where the charged particles interact with the induced RF waves, was increased by replacing tapered cavities with single-stepped cavities in a 12-cavity rising-sun relativistic magnetron with diffraction output (RMDO) that the electronic efficiency of
$\pi $
-mode generation in a 12-cavity rising-sun RMDO with single-stepped cavities driven by a transparent cathode
[6]
with gigawatt output power level can be as high as 83% for
$\alpha = 12.5^{\circ }$
, 79% for
$\alpha = 17.5^{\circ }$
, and 82% for
$\alpha = 18.2^{\circ }$
at
$\beta = 32^{\circ }$
, where
$\alpha $
is the angle between the inner wall and the
$z$
-axis, and
$\beta $
is the angle between the outer wall and the
$z$
-axis. When
$\alpha $
, the angle between the inner wall and the
$z$
-axis, is changed, the depth of single-stepped cavities was changed. This would lead to the coupling between deep cavities and shallow cavities in the 12-cavity rising-sun MDO changing too, and which finally results in different frequencies of magnetron operation in the
$\pi $
-mode. As we know, gigawatt nanosecond output power pulse is useful for the nanoradar system, and our PIC simulations found that when a 400-kV voltage pulse of 10-ns duration is applied to a 12-cavity rising-sun MDO driven by a transparent cathode or a solid cathode, the output power of the
$\pi $
-mode can be as high as 1.5 GW. Without loss of generality, for
$\alpha = 12.5^{\circ }$
and
$\beta = 32^{\circ }$
, the peak efficiency of
$\pi $
-mode generation in a 12-cavity rising-sun MDO with single-stepped cavities design is around 82% and occurs for voltage
$V\sim 400$
kV ± 50 kV. This paper describes optimizing the parameters in a 12-cavity rising-sun RMDO for the desired
$\pi $
-mode operation.