An Unmagnetized Plasma-Loaded Relativistic Backward-Wave Oscillator: Experiment and Simulation

Reported in this paper are the results of an experiment to produce high-power microwave radiation from a gas-filled backward wave oscillator (BWO) driven by a relativistic electron beam without external guiding magnetic field. A peak power for background gas pressure at 5.25 mTorr has been observed as argon pressure from 0.75 mTorr to 15 mTorr. Operating frequency of the oscillator has been measured at 9.6 ± 0.4 GHz. The results of PIC simulation are in good agreement with the experimental results. A reasonable explanation is given for experimental results by PIC simulation.     

Chaos and Hyperchaos in a Backward-Wave Oscillator

Based on a numerical solution of the equations of the nonstationary nonlinear theory, we study chaotic self-oscillation regimes in a backward-wave oscillator. For “weak” chaos, arising via a period-doubling cascade of self-modulation for moderate values of the normalized-length parameter, and for developed chaos, which corresponds to large values of this parameter, we present the temporal dependences of the output-signal amplitude, the phase portraits, and the statistical parameters of the dynamics. It is shown that developed chaos is characterized by the presence of more than one positive Lyapunov exponent (hyperchaos). We also present estimates of the Kolmogorov–Sinai entropy, the Lyapunov dimension, and the correlation dimension obtained from the Grassberger–Procaccia algorithm. The results confirm that a finite-dimensional strange attractor is responsible for the chaotic regimes in a backward-wave oscillator.     

Generation of a Periodic Sequence of High-Power Ultrashort Pulses in a Chain of Coupled Backward-Wave and Traveling-Wave Tubes Operating in the Regimes of Amplification and Nonlinear Kompfner Suppression

We have studied the dynamics of an electronic microwave generator with backward-wave and traveling-wave tubes connected in the feedback circuit and operating in the regimes of amplification and nonlinear Kompfner absorption, respectively. It is shown that radiation generated in such a system can have the form of a periodic sequence of ultrashort pulses. The studied mechanism of pulse generation is analogous to the method of passive mode locking, which is widely used in laser physics.     

Study of a X-Bank Relativistic Backward Wave Oscillator with Variable Couple Impedance

An electromagnetic particle-in-cell code has been used to simulate the nonlinear beam wave interaction and other optimization issues of a X-band RBWO with variable couple impedance, the simulation results show: the device can high-efficiently generate microwave radiation of 950MW peak power at (9.06±O.03) GHz when it is driven by a 5KA-500KV annular electron beam, peak power efficiency is 38%. The preliminary experiment results show that the microwave-generating efficiency of the non-uniform impedance RBWO is about twice of the uniform case in the same operating conditions.     

Relativistic Treatment of Spinless Particles Subject to a Tietz-Wei Oscillator

The bound state solutions of the relativistic Klein-Gordon equation with the Tietz-Wei diatomic molecular potential are presented for the s wave. It is shown that the solutions can be expressed by the generalized hypergeometric functions. The normalized wavefunctions are also derived.     

Relativistic Treatment of Spinless Particles Subject to a Tietz-Wei Oscillator

The bound state solutions of the relativistic Klein-Gordon equation with the Tietz-Wei diatomic molecular potential are presented for the s wave. It is shown that the solutions can be expressed by the generalized hypergeometric functions. The normalized wavefunctions are also derived.     

带有反射腔的相对论返波管初步实验研究

阐述了带有反射腔的相对论返波管的初步实验研究进展。反射腔是一段不规则的圆波导,在相对论返波管中起到截止颈的作用。初步实验的结果为：外加磁场Bz =0.82T时,输出微波功率为170MW,微波频率8.874GHz,脉宽为10ns;外加磁场Bz =1.7T时,微波功率为370MW,频率与脉宽不变;根据辐射场功率密度分布判定传输模式为TM01模。结果表明：带有反射腔的返波管在较低外加磁场下也能够工作。     

Analytical and Numerical Studies for Chaotic Dynamics of a Duffing Oscillator with a Parametric Force

The chaotic dynamics of a Duffing oscillator with a parametric force is investigated. By using the direct perturbation technique, we analytically obtain the general solution of the 1st-order equation. Through the boundedness condition of the general solution we get the famous Melnikov function predicting the onset of chaos. When the parametric and external forces are strong, numerical simulations show that increasing the amplitude of the parametric or external force can lead the system into chaos via period doubling.     

Analytical and Numerical Studies for Chaotic Dynamics of a Duffing Oscillator with a Parametric Force

The chaotic dynamics of a Duffing oscillator with a parametric force is investigated. By using the direct perturbation technique, we analytically obtain the general solution of the lst-order equation. Through the boundedness condition of the general solution we get the famous Melnikov function predicting the onset of chaos. When the parametric and external forces are strong, numerical simulations show that increasing the amplitude of the parametric or external force can lead the system into chaos via period doubling.     

Generation of Microwave Pulses with a Carrier Frequency of 3.8 GHz and a Length of 75 ns by a Relativistic Cherenkov Microwave Oscillator without a Guiding Magnetic Field

In the experiment with an electron energy of ≈500 keV, the long-pulse (~300T, where T is the oscillation period) the generation regime of a relativistic Cherenkov microwave oscillator without a guiding magnetic field at a carrier frequency of 3.8 GHz has been obtained. A high-power microwave radiation pulse length of ~75 ns, a peak generation power of 210 ± 30 MW, and a power conversion efficiency of 9 ± 2% were attained.     

Chaotic Solutions of a Typical Nonlinear Oscillator in a Double Potential Trap

We have obtained a general unstable chaotic solution of a typical nonlinear oscillator in a double potential trap with weak periodic perturbations by using the direct perturbation method. Theoretical analysis reveals that the stable periodic orbits are embedded in the Melnikov chaotic attractors. The corresponding chaotic region and orbits in parameter space are described by numerical simulations.     

Relativistic Treatment of Spinless Particles Subject to a Rotating Deng-Fan Oscillator

The bound state solutions of the Klein-Gordon equation with the rotating Deng-Fan molecular potential are presented by using a proper approximation to the centrifugal term within the framework of equal scalar and vector Deng-Fan potentials. It is shown that the solutions can be expressed by the generalized hypergeometric functions. The normalized wavefunctions are also derived.     

粒子群及遗传算法在相对论返波管中的应用

在全三维粒子模拟软件CHIPIC平台上,分别开发了粒子群及基因算法模块.以相对论返波管为例,采用三种不同类型的参数(连续参数、离散参数、混合参数),对粒子群及基因算法进行比较.优化结果表明:粒子群算法的收敛速度更快,在有限的迭代步数内得到的目标结果也更优良,总体表现优于基因算法.     

Coherent States and a Path Integral for the Relativistic Linear Singular Oscillator

The SU（1,1） coherent states for a relativistic model of the linear singular oscillator are considered. The corresponding partition function is evaluated. The path integral for the transition amplitude between SU（1,1） coherent states is given. Classical equations of the motion in the generalized curved phase space are obtained. It is shown that the use of quasiclassical Bohr Sommerfeld quantization rule yields the exact expression for the energy spectrum.     

相对论谐振子下的自旋和赝自旋轨道伙伴态劈裂

通过求解具有谐振子势的径向标量势与矢量势的Dirac方程, 分别分析了原子核中赝自旋和自旋双重态的能级劈裂和波函数劈裂随着谐振子的振动频率参数ω和描述谐振子势阱底偏离中心参数r₀的变化关系. 研究发现, 这些参数对于赝自旋和自旋双重态的能级劈裂和波函数劈裂都有着显著的影响. 此外, 也研究了能级劈裂和波函数劈裂随着量子数的变化关系. 由于参数ω与核子数有关, 而参数r₀与形变核有关, 所以以这些参数为变量对于赝自旋劈裂和自旋劈裂的研究是有意义的, 研究的结果至少可以定性地应用到大部分原子核中.     

Gyrotron Backward Wave Oscillator Experiments with a Relativistic Electron Beam Using an X-Band Rectangular Waveguide

A mildly relativistic electron beam (500keV, 200A, 10ns) injected into an X-band rectangular waveguide immersed in a uniform axial magnetic field (4-10kG) produced magnetically tunable microwave radiation in the 9-13 GHz frequency range with an estimated output power of 1MW. The frequency range and tunability of the radiated microwave agreed with a theoretical model for a gyrotron backward wave oscillator taking into account the low energy component of the beam electron.