Abstract:
Work was begun on the design of a novel 140GHz Gyroklystron
Amplifier in the Waves and Beams division of the Plasma Science and
In addition to design work which will count toward a Master’s Thesis, preparation work was done to pave the way for experimental Doctorate work to start in approximately one year.
Introduction:
In a gyroklystron, electrons emitted from an annular cathode spiral along the axial magnetic field lines in a solenoidal magnet. At the center of the magnet, there electrons pass through an alternating series of resonant cavities and drift tubes, in which a low power RF signal is amplified to the desired power level by radiating power at the relativistic cyclotron frequency determined by the magnetic field strength. For the operating frequency of 140 GHz and a relativistic gamma of around 1.04, approximately 52 kG (5.2 T) magnetic field is required. The essential components of this gyroklystron are outlined in Figure 1. These components include the electron gun, a copper-wound auxiliary solenoid centered on the gun, the cavity resonators, the collector, the input and output waveguides, an ion pump and the high field superconducting magnet.
Electron Gun:
The electron gun consists of a heated cathode brought to a high voltage (in an absolute sense) of -10 kV to -40 kV for this experiment (not yet determined). The high electric field between this heated cathode and the nearby grounded anode cause electrons to be pulled off to weakly relativistic velocities of around gamma = 1.04, or about 20% of the speed of light. The electron beam quality must be very good in order to produce clean amplification. A good beam quality is characterized by a low velocity spread, which is defined as ratio of the standard deviation of parallel velocity to the parallel velocity and it typically less than 8% for good quality. The physical construction of the cathode / anode structure causes electrons to inherit two separate velocities, perpendicular and parallel. The ratio of these velocities, that is vperpendicular / vparallel is defined as the beam α (alpha) and is typically between 1.2 and 1.6. Higher beam α leads to much higher gain, but also higher detrimental effects of velocity spread. The beam energy transferred to the electromagnetic waves is governed by the perpendicular velocity.
The electron gun design for this project largely depends on the operation voltage, which has not yet been decisively determined. There are several existing electron guns available for this project that may be suitable for this application. If certain characteristics cannot be found in these MIT-owned electron guns, a new one will be designed using the EGUN electron gun simulation code.
Cavities:
The gyroklystron will consist of probably five or six resonant cavities, each of which has varying functions. The first cavity is the so-called input cavity where a low power electromagnetic wave is injected and interacts with the electron beam. In phase space, the electron beam is deformed by this interaction and begins to “bunch,” emitting cyclotron radiation in phase coherently. A convective instability results as the electron beam travels through the intermediate cavities. The relative amplitude of the electromagnetic radiation in each cavity grows as a result of this instability. In the final cavity (the “extraction” cavity), the electromagnetic fields are carried out by means of diffractive coupling to the output waveguide.
Figure 1: Essential components of the Gyroklystron.
The essential feature of these cavities will be there construction using a Photonic Band Gap (PBG) waveguide structure. Such a structure consists of a periodic lattice of rods with a defect in the center that is used for trapping the electromagnetic fields. This method has been shown to be a feasible and effective way of reducing mode competition in overmoded structures.
The Collector:
The purpose of the collector is to provide a means of dispensing with the spent electron beam after the interactions are complete. The collector must be able to handle the heat loading of a weakly relativistic electron beam and must be properly designed to avoid incurring any hot spots, which leads to an outgassing phenomenon that can effectively poison the operation.
Input and output waveguides:
The input power signal will come from a solid-state, 4-phase pulse forming network consisting of a Gunn diode to injection lock an IMPATT diode for good frequency stability. Because this system has a limited output power of around 50mW, every effort must be made to ensure that very little power is lost. Hence both the input and output waveguides will be probably be overmoded Gaussian modes to lower losses and facilitate passage through the vacuum window with low loss.
Ion pump:
The
ion pump is used after a turbo pump has removed most of the fluid air from the
tube jacket vacuum chamber. In order to
reduce the pressure to the necessary low operating levels of around 10-7
to 10-9 Torr, the ion pump is used.
The ion pump traps molecules electrostatically by implanting them into
its titanium surface. The operation of
the gyroklystron usually causes heating in local areas that leads to
outgassing. Therefore, the ion pump must
be large enough to handle common outgassing loads.
The Magnet:
The magnet itself is a very important feature of the gyroklystron operation. It must be strong enough to cause the electrons to emit cyclotron radiation at the desired frequency of 140GHz and it must have a long length of uniformity throughout the cavity structure. The tolerance of this uniformity should be within +/-0.5% in order to prevent the formation of disabling oscillations in the amplifier.
The magnet will be ordered shortly to satisfy our requirements. The lead time for building such a magnet is approximately one year, which should coincide with the anticipated beginning of the experimental Doctoral studies.
Summary of work to date:
Electron gun:
No significant work has been made on the electron gun yet. Detailed design work cannot be made until the nominal operation voltage and current have been chosen.
Cavities:
A number of theories have been explored to model the behavior of the cavity structure under a range of operation parameters. The cavities are perhaps the most important part of the system, so a significant amount of time has been spent writing computer codes to solve for the operation characteristics in these cavities. Two regimes exist: A linear regime for all cavities but the extraction cavity, and a non-linear regime for the extraction cavity. Non-linear code could be used for all cavities, but is much more complex to implement for such a wide range of field strengths in the different cavities.
Figure 2: Sample output figure of Linear Code. Top, left: Normalized field in cavities, F; top right: bunching parameter in cavities, q; bottom left: Gain versus detuning, Δ; bottom right: detuning, Δ, versus cavity length.
A sample figure from the linear code that was written this summer is shown in Figure 2 and shows the normalized field strength and bunching parameter as they progresses through the cavities, the gain versus detuning parameter, and the detuning parameter versus cavity length. The cavity length has a strong effect on the gain, and so this process is a circular one of reconciling these parameters.
A figure from the non-linear code is shown in Figure 3. There is a local efficiency maximum around the mu = 2.1 and F = 0.39 region. This efficiency parameter describes the interaction between the electron beam, which is coherently emitting radiation at the cyclotron frequency, and the RF fields in the cavity. A high efficiency means more power can be extracted from the electron beam. The peak efficiency is around 90.7%, which is much higher than the 70% efficiency achievable in a gyrotron oscillator. This high efficiency zone cannot be realized in a gyroklystron amplifier because the operation current necessary to reach this zone is above the starting current for fatal oscillations in the amplifier. Our target efficiency is greater than 35%.
Figure 3: Nonlinear code plots showing a local efficiency maximum around mu = 2.1 and F = 0.39. The corresponding q, delta and psi values are shown on the other subplots.
These cavities will be constructed from the PBG lattice, so one major issue has been the feasibility of trapping certain modes. From our initial studies, the TE04 mode and TE02 mode can be trapped cleanly. Due to the behavior of PBG, the TE03 mode could not be confined cleanly using either a square lattice or triangular lattice. Furthermore, a lower operating mode such as TE02 or TE03 is preferred because the gain in the gyroklystron is much higher for lower modes. The higher modes, such at TE04 can handle much more power due to their larger diameters. The TE01 mode would have a distorted shape in the PBG structure and would thus not couple efficiently. Figure 4 shows a preliminary HFSS simulation of the TE02 mode properly confined in the PBG defect using a triangular lattice. Further adjustments need to be done in order to prevent the leakage evident in the lattice, but the TE02 shape is well intact, which will lead to good beam-wave coupling.
Figure 4: A preliminary HFSS simulation of the clean TE02 mode trapped in the PBG.
The Collector:
No significant work has been done yet on the collector. The design will depend largely on the operation voltage and current parameters yet to be decided on. A preliminary study showed that collector design should not be unusually difficult since the power levels are relatively low.
Input and output waveguides:
The input and output waveguides will likely be an overmoded circular copper waveguide carrying a Gaussian mode. The more difficult part will be designing the method for coupling the power from the waveguide into / out of the electron beam. Using the PBG waveguide, rods in the lattice can be removed in the periphery to facilitate injection / extraction of electromagnetic waves normally trapped by the PBG structure.
The Magnet:
The magnet will be required for the experimental Doctoral studies to be pursued after completion of the Master’s Degree. Because the lead time for a magnet is approximately one year, the magnet will be ordered in early September 2003. Thus specifications for the magnet needed to be carefully chosen this summer. Several preliminary gyroklystron designs were collected to decide on the requirements for the magnet. The length of the uniform field was chosen based on the amount of gain that would be needed in the cavities. Contacts were made in industry for assistance with gathering these specifications.
Next Steps:
The code models still need to be benchmarked and verified. The models still lack several effects that should be included, such as velocity spread and frequency shift due to the presence of the electron beam. The design process will consist of a series of iterations before converging onto a solid design.
After the codes have been established, more works will be carried out in HFSS to simulate the full three-dimensional cavity structures. These 3-D simulations are necessary because of the complexity of the PBG structures. Furthermore, the design of the input and output couplers with their mode conversion details will be an involved process.