Two types of dielectric wall accelerator (DWA) structures, a bi-polar Blumlein line and zero integral pulse line (ZIP) structures were investigated. The high gradient insulator simulated by the particle in cell code con rms that it has little in uence on the axial electric field. The results of simulations using CST microwave studio indicate how the axial electric field is formed, and the electric eld waveforms agree with the theoretical one very well. The in uence of layer-to-layer coupling in a ZIP structure is much smaller and the electric eld waveform is much better. The axial of the Blumlein structure's electric field has better axial stability. From both of the above, it found that for a shorter pulse width, the axial electric field is much higher and the pulse stability and delity are much better. The CST simulation is very helpful for designing DWA structures.
PCAS:
In [1], we examined the effects of dark energy on the gravitational energy for the quintessential charged-Kerr black holes by approximate Lie symmetry approach. It was shown that the gravitational energy of the charged-Kerr black hole spacetime surrounded by dark energy decreased due to the presence of the cosmological constant (ωc=−1) and quintessence dark energy (ωq=−23) [1]. Whereas, for the case of frustrated network of cosmic strings (ωn=−13) the contribution in energy of the charged-Kerr black hole due to the presence of dark energy term En was observed to be positive for different values of dark energy parameter α (as shown in FIG. 7.) while FIG. 8. shows the effect of dark energy with different values of spin a. We observed there, that if the dark energy parameter α is initially small, then the value of En will increase primarily and then it showed a gradual decline for the larger values of α [1]. This result needs correction.
Therefore in this corrigendum, we present the effects of dark energy on the energy content of the charged-Kerr black hole surrounded by the dark energy for ωn=−13. It is observed that at this value of the equation of state parameter, the presence of the dark energy first decreases the energy content of the charged-Kerr black hole surrounded by the dark energy and then increases the energy. This is shown by the graphical results.
I.
GRAVITATIONAL ENERGY OF THE QUINTESSENTIAL CHARGED-KERR BLACK HOLE FOR ωn=−13
As shown in [1], in the case of ωn=−13, we get the following re-scaling factor of energy for the charged-Kerr spacetime surrounded by dark energy
MC−K−n=M2r[1−Q22M2]+3Ma4r2+Mα2r[11−α−a2r]
(1)
It was observed, for ωn=−13, the total energy in the charged-Kerr spacetime surrounded by dark energy varies from the energy in the charged-Kerr spacetime by the following expression [1]
En=Mα2r[11−α−a2r]
(2)
In order to analyze the significant features of dark energy, we sketch the expression (2) versus α and radial distance r.
From FIG. 1, it is observed that for some values of α and for smaller values of r the value of En is negative which shows that it decreases the energy content of the underlying spacetime, and for some values of α and relatively bigger values of r, the value of En is positive and hence increases the energy content of the CK spacetime (as evident from (1)). Hence, we observe that the contribution of dark energy term for ωn=−13, first decreases the total energy of the underlying spacetime for smaller values of radial coordinate r and then increases for comparatively larger values of r. FIG. 2 depicts the increasing behavior of En for different values of spin parameter a.
Figure 1
Figure 1.
(color online) plots showing the behavior of En for the quintessential charged-Kerr black hole for ωn=−13 with different values of α and a fixed value of M=1, a=0.4.
Figure 2.
(color online) plots showing the behavior of En for the quintessential charged-Kerr black hole for ωn=−13 with different values of a, 0<α<1/2 and a fixed value of M=1 and r=0.4.
Therefore, in view of the above discussion it is concluded that the result given in [1] must be stated as
Remark:The effect of cosmological constant and quintessence decreases the energy of the charged-Kerr black hole surrounded by dark energy, whereas the effect of a frustrated network of cosmic strings decreases the energy of the charged-Kerr black hole surrounded by dark energy for some values ofαand for smaller values ofrand increases the energy for some values ofαand relatively bigger values ofras evident from(1).
References
[1]
George J Caporaso, Sampayan S, CHEN Y J et al. Particle Accelerator Conference, 2007, PAC. IEEE, 2007. 857-8612 Sampayan S, Caporaso G, CHEN Y J et al. Plasma Science,2007. ICOPS 2007. IEEE 34th International Conference on,2007. 6833 CHEN Yu-Jiuan, Paul A C. Particle Accelerator Conference, 2007, PAC. IEEE, 2007. 1787-17894 Harris J R, Kendig M, Poole B et al. Applied Physics Letters, 2008, 83: 2415025 Joler, Miroslav. Analysis and Optimization of ParallelPlate Blumlein Line for Compact Pulsed-Power system, (Ph.D.Thesis). The University of New Mexico, AAT3220947, 2006. 2646 ZHAO Quan-Tang, YUAN Ping, ZHANG Zi-Min et al. Chinese Physics C, 2011, 35(12): 1148-11517 Sampayan S, Caporaso G, Carder B et al. Particle Accelerator Conference, 1995. Proceedings of the 1995, 1995, 2:1269-12718 ZHAO Quan-Tang, YUAN Ping, ZHANG Zi-Min et al. High Power Laser and Particle Beams. 2011, 23(6): 1629 (in Chinese)9 Nelson S D, Poole B R, Caporaso G J. Particle Accelerator Conference, PAC. IEEE, 2007. 1784-1786
References
[1]
George J Caporaso, Sampayan S, CHEN Y J et al. Particle Accelerator Conference, 2007, PAC. IEEE, 2007. 857-8612 Sampayan S, Caporaso G, CHEN Y J et al. Plasma Science,2007. ICOPS 2007. IEEE 34th International Conference on,2007. 6833 CHEN Yu-Jiuan, Paul A C. Particle Accelerator Conference, 2007, PAC. IEEE, 2007. 1787-17894 Harris J R, Kendig M, Poole B et al. Applied Physics Letters, 2008, 83: 2415025 Joler, Miroslav. Analysis and Optimization of ParallelPlate Blumlein Line for Compact Pulsed-Power system, (Ph.D.Thesis). The University of New Mexico, AAT3220947, 2006. 2646 ZHAO Quan-Tang, YUAN Ping, ZHANG Zi-Min et al. Chinese Physics C, 2011, 35(12): 1148-11517 Sampayan S, Caporaso G, Carder B et al. Particle Accelerator Conference, 1995. Proceedings of the 1995, 1995, 2:1269-12718 ZHAO Quan-Tang, YUAN Ping, ZHANG Zi-Min et al. High Power Laser and Particle Beams. 2011, 23(6): 1629 (in Chinese)9 Nelson S D, Poole B R, Caporaso G J. Particle Accelerator Conference, PAC. IEEE, 2007. 1784-1786
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ZHAO Quan-Tang, ZHANG Zi-Min, YUAN Ping, CAO Shu-Chun, SHEN Xiao-Kang, JING Yi, LIU Ming and ZHAO Hong-Wei. Electromagnetic simulation study of dielectric wall accelerator structures[J]. Chinese Physics C, 2012, 36(4): 350-354. doi: 10.1088/1674-1137/36/4/010
ZHAO Quan-Tang, ZHANG Zi-Min, YUAN Ping, CAO Shu-Chun, SHEN Xiao-Kang, JING Yi, LIU Ming and ZHAO Hong-Wei. Electromagnetic simulation study of dielectric wall accelerator structures[J]. Chinese Physics C, 2012, 36(4): 350-354.
doi: 10.1088/1674-1137/36/4/010
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Abstract: Two types of dielectric wall accelerator (DWA) structures, a bi-polar Blumlein line and zero integral pulse line (ZIP) structures were investigated. The high gradient insulator simulated by the particle in cell code con rms that it has little in uence on the axial electric field. The results of simulations using CST microwave studio indicate how the axial electric field is formed, and the electric eld waveforms agree with the theoretical one very well. The in uence of layer-to-layer coupling in a ZIP structure is much smaller and the electric eld waveform is much better. The axial of the Blumlein structure's electric field has better axial stability. From both of the above, it found that for a shorter pulse width, the axial electric field is much higher and the pulse stability and delity are much better. The CST simulation is very helpful for designing DWA structures.
ZHAO Quan-Tang, ZHANG Zi-Min, YUAN Ping, CAO Shu-Chun, SHEN Xiao-Kang, JING Yi, LIU Ming and ZHAO Hong-Wei. Electromagnetic simulation study of dielectric wall accelerator structures[J]. Chinese Physics C, 2012, 36(4): 350-354.
doi: 10.1088/1674-1137/36/4/010