Exact Relativistic Solution for the One-Dimensional Diode

Jory, H.; Trivelpiece, A. W.

doi:10.1063/1.1657117

Cited by 140 publications

(49 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For all other profiles, similar clamping effects due to space charge repulsion are observed from the results. Based on these simulations, we conclude that time-varying injection seems unlikely to contribute more than the space-charge limit (6). This is the main result of this paper.…”

Section: A Classical Casesupporting

confidence: 59%

“…This is when the SC limit dominates the electron flow process and the virtual diode forms. It is also speculated that the zero cathode field E C ¼ 0 is not a critical condition for the space charge limit for time-varying 2017) injection cases, as previous work 6,22 consider so. We speculate that the time-dependent space-charge limit may involve a more dynamic process of the virtual cathode than a static zero cathode field.…”

Section: Time-dependent Quantitiesmentioning

confidence: 92%

“…For a diode with a gap spacing of d and a diode voltage of / g , this is known as the well-known Child-Langmuir law. [1][2][3] This law extends to the more general case of nonzero initial velocity v 0 4,5 and the relativistic regime [6][7][8][9][10] when the voltage potential becomes relativistic. In recent years, the efforts to achieve a higher electron flow have been very active, in both classical and relativistic regimes.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Space-charge effect of the time-varying electron injection in a diode: Classical and relativistic regimes

Tang

2017

Physics of Plasmas

View full text Add to dashboard Cite

Section: A Classical Casesupporting

confidence: 59%

Section: Time-dependent Quantitiesmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Space-charge effect of the time-varying electron injection in a diode: Classical and relativistic regimes

Tang

2017

Physics of Plasmas

View full text Add to dashboard Cite

“…Equation ͑1͒ is derived by assuming zero electron emission velocity and neglecting relativistic effects. Later an analytical solution for limiting current of relativistic electron flow in the planar diode was found, 3 but with the generalization of Child-Langmuir law in two dimensions still remaining a formidable task analytically. So an alternative approach was adopted, namely, the use of particle-in-cell ͑PIC͒ computer simulation to investigate two-dimensional space-chargelimited flow in a planar diode.…”

mentioning

confidence: 99%

Space-charge-limited current in cylindrical diodes with finite-length emitter

Kostov

Barroso

2002

Physics of Plasmas

View full text Add to dashboard Cite

In the present paper we extend to two dimensions the classical Langmuir-Blodgett law, which determines the maximum current I LB that can be accelerated by a given voltage across two infinitely long coaxial cylinders. Generalization of the I LB law is established by performing two-dimensional 2D particle-in-cell numerical experiments on a variety of cylindrical diode configurations with a finite-length emitter. It is found that the limiting current in two dimensions I 2D follows a monotonically decreasing function of the emitter length-to-outer electrode radius ratio L/R as expressed by the fitting function I 2D /I LB ϭ1ϩ0.1536/(L/R)ϩ0.0183/(L/R) 2 within 2.5% accuracy for simulation data in which the ratio of the outer to inner radii exceeds 3. © 2002 American Institute of Physics. ͓DOI: 10.1063/1.1446876͔The effect of space charge on the flow of charged particles between two parallel electrodes in vacuum is of great importance in microwave electronics, crossed-field devices, and high-power diodes. In particular, if too much charge is injected into a gap, the resulting electric field becomes sufficiently high to reflect the injected particles back to the emitter, forming a virtual cathode. Limiting currents of vacuum diodes are classical subjects with early works dating back to the beginning of the last century when onedimensional space-charge-limited flow solutions were derived. Only for simple cases, however, such as plane parallel plates, infinitely long coaxial cylinders, and concentric sphere there exist analytical solutions.1 For a planar gap with gap separation D and gap voltage V, the maximum electron current density in a space-charge-limited diode is given by the well-known Child-Langmuir law,where e and m are, respectively, the charge and the mass of the emitted particles, and ⑀ 0 is the free space permittivity. Equation ͑1͒ is derived by assuming zero electron emission velocity and neglecting relativistic effects. Later an analytical solution for limiting current of relativistic electron flow in the planar diode was found, 3 but with the generalization of Child-Langmuir law in two dimensions still remaining a formidable task analytically. So an alternative approach was adopted, namely, the use of particle-in-cell ͑PIC͒ computer simulation to investigate two-dimensional space-chargelimited flow in a planar diode.4,5 About works on cylindrical diodes, particle simulation method was successfully applied for studying the stability of divergent and convergent electron flows in 1D cylindrical Pierce diode. 6 Also numerical experiments were performed to examine electrical properties of charged-particle flows in high-power cylindrical pinchedbeam diode over a wide range of voltages. 7The electron flow between coaxial cylinders is another important topic on beam formation theory, which has laid the basis of many useful gun designs. High-power cylindrical diodes have also found application in cylindrical vircators 8 and in high-resolution radiography sources.9 Again, as for the planar diode, the specialized lit...

show abstract

“…Space charge limited (SCL) flow in diodes has been an area of active research since the pioneering work of Child and Langmuir [10,11]. The scope of the theory was later extended in order to incorporate other physical mechanisms such as relativistic behavior [12] or quantum mechanical effects [13], although the modeling was limited to a one-dimensional treatment of the SCL flow. In 2001, Lau first introduced a simple analytical theory for two-dimensional Child Langmuir law [14] which proved to be in good agreement with the simulation data obtained by Luginsland [15].…”

Section: Introductionmentioning

confidence: 99%

High power electron diode for linear induction accelerator at a flash radiographic facility

Plewa

Bernigaud

Barnes

et al. 2018

Phys. Rev. Accel. Beams

View full text Add to dashboard Cite

We investigated a new cathode design and beam transport with the EPURE axis-1 injector in order to increase the beam characteristics at 3.8 MeV, 80 ns FWHM from the 2.0 kA nominal current to 2.6 kA corresponding to an average current density of 82 A=cm 2 . Such current increase is highly desirable for improving the x-ray dose and hence radiographic performances. To achieve this, a time-dependent model based on the particle-in-cell method was developed in order to simulate the injector. Using results from calculations based on this model, a 17.2 cm AK gap diode with a larger radius cathode (3.175 cm) was designed, manufactured and tested. Experimental and calculated currents and emittances are qualitatively compared. The study provides a detailed understanding of the beam dynamics inside this type of high current, high energy injector.

show abstract

Exact Relativistic Solution for the One-Dimensional Diode

Abstract: Exact relativistic solutions for the one-dimensional space-charge-limited diode, and for the one-dimensional diode with finite field at the cathode plane are given. The results are compared with approximate solutions which are useful in different energy ranges.

Cited by 140 publications

References 3 publications

Space-charge effect of the time-varying electron injection in a diode: Classical and relativistic regimes

Space-charge effect of the time-varying electron injection in a diode: Classical and relativistic regimes

Space-charge-limited current in cylindrical diodes with finite-length emitter

High power electron diode for linear induction accelerator at a flash radiographic facility

Contact Info

Product

Resources

About