For t≥2, the t-independence complex Indt(G) of a graph G is the collection of all A⊆V(G) such that each connected component of the induced subgraph G[A] has at most t−1 vertices. The topology of Indt(G) is intimately related to the combinatorial property of G. In this paper, we consider the Stanley–Reisner ideal Jt(G) of Indt(G) and focus on its algebraic properties. We prove that for a chordal graph G and for all t, reg(R/Jt(G))=(t−1)νt(G) and pd(R/Jt(G))=bight(Jt(G)), where νt(G) denotes the induced matching number of the corresponding hypergraph of Jt(G), and reg, pd and bight stand for the regularity, projective dimension and big height, respectively. As a consequence of the above results, we combinatorially characterize when the Stanley–Reisner ideal of the t-independence complex of a chordal graph has a linear resolution as well as when it satisfies the Cohen–Macaulay property. The above formulas and their consequences can be seen as a nice generalization of the classical results corresponding to the edge ideals of chordal graphs.

Let G be a simple graph and It(G) denote the t-path ideal of G. It is well known that the Castelnuovo–Mumford regularity reg(R/It(G)) and the projective dimension pd(R/It(G)) are bounded below by the quantities (t-1)νt(G) and the big height bight(It(G)), respectively, where νt(G) denotes induced matching number of the hypergraph corresponding to It(G). We show that if t≥4, then the difference between reg(R/It(G)) and (t-1)νt(G), and the difference between pd(R/It(G)) and bight(It(G)) can be arbitrarily large even if we take G to be a tree. This, in particular, disproves a conjecture in Hang and Vu (Graphs Combin 41(1):18, 2025). However, when t=3 and G is chordal, we show that reg(R/I3(G))=2ν3(G) and pd(R/I3(G))=bight(I3(G)), extending the well-known formulas for the edge ideals of chordal graphs. As a consequence, we get that the 3-path ideal of a chordal graph is Cohen–Macaulay if and only if it is unmixed. Additionally, we show that the Alexander dual of I3(G) is vertex splittable when G is a tree, thereby resolving the t=3 case of a recent conjecture in Abdelmalek et al. (Int J Algebra Comput 33(3):481–498, 2023). Also, for each t≥3, we give examples of chordal graphs G such that the duals of the corresponding t-path ideals are not vertex splittable. Furthermore, we extend the formula of the regularity of 3-path ideals of chordal graphs to all t-path ideals of caterpillar graphs.

Let G be a finite simple graph on the vertex set V(G) and let r be a positive integer. We consider the hypergraph Conr(G) whose vertices are the vertices of G and the (hyper)edges are all A⊆V(G) such that |A|=r+1 and the induced subgraph G[A] is connected. The (hyper)edge ideal Ir(G) of Conr(G) is also the Stanley-Reisner ideal of a generalisation of the independence complex of G, called the r-independence complex Indr(G). In this article we make extensive use of the Mayer-Vietoris sequence to find the graded Betti numbers of Ir(G1∗G2) in terms of the graded Betti numbers of Ir(G1) and Ir(G2), where G1∗G2 is the join of G1 and G2. Moreover, we find formulas for the graded Betti numbers and the Castelnuovo-Mumford regularity of Ir(G) when G is a complete graph, complete multipartite graph, cycle graph, and the wheel graph.

Let G be a finite simple graph, and let NI(G) denote the closed neighborhood ideal of G in a polynomial ring R. We show that if G is a forest, then the Castelnuovo–Mumford regularity of R/NI(G) is the same as the matching number of G, thus proving a conjecture of Sharifan and Moradi in the affirmative. We also show that the matching number of G provides a lower bound for the Castelnuovo–Mumford regularity of R/NI(G) for any G. Furthermore, we prove that if G contains a simplicial vertex, then NI(G) admits a Betti splitting, and consequently, we show that the projective dimension of R/NI(G) is also bounded below by the matching number of G, if G is a forest or a unicyclic graph.

Given a connected graph G on the vertex set {0,1,…,n} with the root vertex 0, Postnikov and Shapiro associated a monomial ideal MG in the polynomial ring R=K[x1,…,xn] over a field K such that the vector space dimension of R/MG is same as the determinant of the reduced Laplacian of G. Dochtermann introduced the 1-skeleton ideal MG(1)⊂MG which satisfies the property that the vector space dimension of R/MG(1) is bounded below by the determinant of the reduced signless Laplacian of G. In this paper, we characterize all subgraphs of the complete multigraph Kn+1a,1, in particular all simple graphs G, such that the vector space dimension of R/MG(1) is same as the determinant of the reduced signless Laplacian.

A celebrated theorem of Fröberg gives a complete combinatorial classification of quadratic square-free monomial ideals with a linear resolution. A generalization of this theorem to higher degree square-free monomial ideals is an active area of research. The existence of a linear resolution of such ideals often depends on the field over which the polynomial ring is defined. Hence, it is too much to expect that in the higher degree case a linear resolution can be identified purely using a combinatorial feature of an associated combinatorial structure. However, some classes of ideals having linear resolutions have been identified using combinatorial structures. In the present paper, we use the notion of r-independence to construct an r-uniform hypergraph from the given graph. We then show that when the underlying graph is cochordal, the corresponding edge ideal is vertex splittable, a condition stronger than having a linear resolution. We use this result to explicitly compute graded Betti numbers for various graph classes. Finally, we give a different proof for the existence of a linear resolution using the topological notion of r-collapsibility.

Given a finite simple undirected graph G there is a simplicial complex Ind(G), called the independence complex, whose faces correspond to the independent sets of G. This is a well-studied concept because it provides a fertile ground for interactions between commutative algebra, graph theory and algebraic topology. In this paper, we consider a generalization of independence complex. Given r ≥ 1, a subset of the vertex set is called r-independent if the connected components of the induced subgraph have cardinality at most r. The collection of all r-independent subsets of G form a simplicial complex called the r-independence complex and is denoted by Indr(G). It is known that when G is a chordal graph the complex Indr(G) has the homotopy type of a wedge of spheres. Hence, it is natural to ask which of these complexes are shellable or even vertex decomposable. We prove, using Woodroofe's chordal hypergraph notion, that these complexes are always shellable when the underlying chordal graph is a tree. Using the notion of vertex splittable ideals we show that for caterpillar graphs the associated r-independence complex is vertex decomposable for all values of r. Further, for any r ≥ 2 we construct chordal graphs on 2r + 2 vertices such that their r-independence complexes are not sequentially Cohen-Macaulay.

For a graph G on the vertex set {0,1,…,n}, the G-parking function ideal MG is a monomial ideal in the polynomial ring R=K[x1,…,xn] such that the vector space dimension of R/MG is given by the determinant of its reduced Laplacian. For any integer k, the k-skeleton ideal MG(k) is the subideal of MG, where the monomial generators correspond to nonempty subsets of [n] of size at most k+1. For a simple graph G, Dochtermann conjectured that the vector space dimension of R/MG(1) is bounded below by the determinant of the reduced signless Laplacian. We show that the Dochtermann conjecture holds for any (multi) graph G. More generally, we prove that this bound holds for ideals JH defined by a larger class of symmetric positive semidefinite n×n matrices H.

Let G be a group and φ be an automorphism of G. Two elements x,y G are said to be φ-twisted conjugate if y = gxφ(g)-1 for some g G. We say that a group G has the R∞-property if the number of φ-twisted conjugacy classes is infinite for every automorphism φ of G. In this paper, we prove that twisted Chevalley groups over a field k of characteristic zero have the R∞-property as well as the S∞-property if k has finite transcendence degree over ℚ or Aut(k) is periodic.

Let Sn be the set of all permutations of [n] = { 1 , … , n} and let W be the subset consisting of permutations σ∈ Sn avoiding 132 and 312-patterns. The monomial ideal IW=〈xσ=∏i=1nxiσ(i):σ∈W〉 in the polynomial ring R= k[x1, … , xn] over a field k is called a hypercubic ideal in Kumar and Kumar (Proc. Indian Acad. Sci. (Math Sci.)126(4) (2016) 479–500). The Alexander dual IW[n] of IW with respect to n= (n, … , n) has the minimal cellular resolution supported on the first barycentric subdivision Bd(Δ n-1) of an n- 1 -simplex Δ n-1. We show that the number of standard monomials of the Artinian quotient RIW[n] equals the number of rooted-labelled unimodal forests on the vertex set [n]. In other words, dimk(RIW[n])=∑r=1nr!s(n,r)=Per([mij]n×n),where s(n, r) is the (signless) Stirling number of the first kind and Per([mij]n×n) is the permanent of the matrix [mij] with mii= i and mij= 1 for i≠ j. For various subsets S of Sn consisting of permutations avoiding patterns, the corresponding integer sequences {dimk(RIS[n])}n=1∞ are identified.

Let G be the circulant graph Cn.S/ with S ⊂ f1; 2; : : : ; b n 2 cg, and let I .G/ denote the edge ideal in the polynomial ring R D KTx0; x1; : : : ; xn-1U over a field K. In this paper we compute the N- graded Betti numbers of the edge ideals of three families of circulant graphs Cn.1; 2; : : : ;bj ; : : : ; b n 2 c/, Clm.1; 2; : : : ; b2l; : : : ; b3l; : : : ; blm 2 c/ and Clm.1; 2; : : : ;bl ; : : : ; b2l; : : : ; b3l; : : : ; blm 2 c/. Other algebraic and combinatorial properties like regularity, projective dimension, induced matching number and when such graphs are well-covered, Cohen-Macaulay, sequentially Cohen-Macaulay, Buchsbaum and S2 are also discussed.

We investigated the role of a guiding magnetic field on extreme ultraviolet (EUV) and ion emission from a laser produced Sn plasma for various laser pulse duration and intensity. For producing plasmas, planar slabs of pure Sn were irradiated with 1064 nm, Nd:YAG laser pulses with varying pulse duration (5-15 ns) and intensity. A magnetic trap was fabricated with the use of two neodymium permanent magnets which provided a magnetic field strength ∼0.5 T along the plume expansion direction. Our results indicate that the EUV conversion efficiency do not depend significantly on applied axial magnetic field. Faraday Cup ion analysis of Sn plasma show that the ion flux reduces by a factor of ∼5 with the application of an axial magnetic field. It was found that the plasma plume expand in the lateral direction with peak velocity measured to be ∼1.2 cm/μs and reduced to ∼0.75 cm/μs with the application of an axial magnetic field. The plume expansion features recorded using fast photography in the presence and absence of 0.5 T axial magnetic field are simulated using particle-in-cell code. Our simulation results qualitatively predict the plasma behavior. © 2014 AIP Publishing LLC.

The design, development and commissioning of 1 MV pulsed electron accelerator producing Flash X-Rays is described in this paper. This pulsed power system is based on bipolar MARX generator and Blumlein followed by Explosive electron emission diode assembly. The peak pulsed power is ∼ 30 GW. The electron energies in the range of 400 keV to 1030 keV are produced and delivered to experimental load of Industrial diode. Electrons are emitted from a stainless steel ring at ground potential by explosive field emission and bombard the anode tungsten pin for flash X-rays generation. The relativistic electron beam has been simulated within the diode chamber and pattern shows the beam propagation. Imaging plates are used to characterize the source size and optimization has been reported. © 2014 IOP Publishing Ltd and Sissa Medialab srl.

We investigated the role of laser pulse duration and intensity on extreme ultraviolet (EUV) generation and ion emission from a laser produced Sn plasma. For producing plasmas, planar slabs of pure Sn were irradiated with 1064 nm Nd:YAG laser pulses with varying pulse duration (5-20 ns) and intensity. Experimental results performed at CMUXE indicate that the conversion efficiency (CE) of the EUV radiation strongly depend on laser pulse width and intensity, with a maximum CE of ∼2.0% measured for the shortest laser pulse width used (5 ns). Faraday Cup ion analysis of Sn plasma showed that the ion flux kinetic profiles are shifted to higher energy side with the reduction in laser pulse duration and narrower ion kinetic profiles are obtained for the longest pulse width used. However, our initial results showed that at a constant laser energy, the ion flux is more or less constant regardless of the excitation laser pulse width. The enhanced EUV emission obtained at shortest laser pulse duration studied is related to efficient laser-plasma reheating supported by presence of higher energy ions at these pulse durations. © 2014 AIP Publishing LLC.

A new computational model to understand the mechanism of discharges along the gas/solid interface at high voltage and high pressure is made based on the models of explosive electron emission, secondary emission, and neutral gas ionization by using finite-difference time domain-based particle-in-cell code. The charge particle movement at different durations is obtained at a pressure of 1 atmosphere. The profiles of phase space, the net charge density along the gap, and the effect of the dielectric on the characteristics of the gas discharge are presented. The ionization coefficient (α) and drift velocity (ve) calculated from simulation data closely match with the existing experimental results. © 1973-2012 IEEE.

This paper deals with the discharge along the surface of angled insulators in compressed gases using 3D finite difference particle-in-cell simulation. The simulation is carried in pure nitrogen at atmospheric pressure. The spacer angle 'θ' is measured between the inclined surface and line vertical to the electrode. The angle is positive when narrow end is connected to the anode and negative when the narrow end is connected to the cathode. The positive spacer angle shows a reduced discharge voltage for a 20mm gap length as compared to the negative spacer angle. © 2013 IEEE.

The low cost and high resolution Multi-gap Resistive Plate Chamber (MRPC) opens up a new possibility to find an efficient alternative detector for the Time of Flight (TOF) based Positron Emission Tomography, where the sensitivity of the system depends largely on the time resolution of the detector. In a layered structure, suitable converters can be used to increase the photon detection efficiency. In this paper results of the cosmic ray test of a four-gap bakelite-based prototype MRPC operated in streamer mode and six-gap glass-based MRPC operated in avalanche mode are discussed. © 2012 Elsevier B.V. All rights reserved.

We present a study of the shot-to-shot variation in frequency of a reflex-triode virtual cathode oscillator with respect to peak diode voltage, current, impedance, and perveance. The typical electron-beam parameters were 185 kV, 7 kA, and 300 ns, with a current density of a few hundreds of amperes per square centimeter. The one-way analysis of variance was employed to examine the statistical correlation of the diode voltage, current, impedance, and perveance with the emitted microwave frequency. It was shown that the microwave dominant frequency variation is statistically correlated only with the peak diode current. However, the secondary emitted frequency is not statistically correlated with any of the electron-beam diode parameters. © 1973-2012 IEEE.

To study the effect of explosive field emission cathodes on high power microwave generation, experiments were conducted on a reflex triode virtual cathode oscillator. Experimental results with cathodes made of graphite, stainless steel nails, and carbon fiber (needle type) are presented. The experiments have been performed at the 1 kJ Marx generator (200Â kV, 300Â ns, and 9Â kA). The experimentally obtained electron beam diode perveance has been compared with the one-dimensional Child-Langmuir law. The cathode plasma expansion velocity has been calculated from the perveance data. It was found that the carbon fiber cathode has the lowest cathode plasma expansion velocity of 1.7Â cm/μs. The radiated high power microwave has maximum field strength and pulse duration for the graphite cathode. It was found that the reflex triode virtual cathode oscillator radiates a single microwave frequency with the multiple needle cathodes for a shorter (<200Â ns full width at half maximum) voltage pulse duration. Copyright © Cambridge University Press 2012.

In an isochronous cyclotron, measurements of central phase of the ion beam with respect to rf and the phase width provide a way to tune the cyclotron for maximum energy gain per turn and efficient extraction. We report here the development of a phase measurement system and the measurements carried out at the Variable Energy Cyclotron Centre's (VECC's) K = 500 superconducting cyclotron. The technique comprises detecting prompt γ-rays resulting from the interaction of cyclotron ion beam with an aluminium target mounted on a radial probe in coincidence with cyclotron rf. An assembly comprising a fast scintillator and a liquid light-guide inserted inside the cyclotron was used to detect the γ-rays and to transfer the light signal outside the cyclotron where a matching photo-multiplier tube was used for light to electrical signal conversion. The typical beam intensity for this measurement was a few times 1011 pps. © 2013 AIP Publishing LLC.

Pulse step modulation (PSM)-based high-voltage power supplies have played a significant role in fusion research. In many cases, multisecondary transformers are used for generation of tens of kilovolt range outputs with fast (microsecond-order) transient response. In this scheme, large numbers of isolated voltage sources are connected in series to generate the output. Isolated voltage sources can be achieved by a large number of separate transformers or by a single unit of multisecondary transformer. Naturally, a transformer having numbers of secondary windings (∼40) on a single core is the preferred solution for PSM topology due to its space and cost consideration. For design and simulation analysis of such a power supply, the model of a multisecondary transformer poses special problem to any circuit analysis software. While many simulation software packages provide transformer models with limited number (3-6) of secondary windings, they still fail to predict the actual observed results from a manufactured unit. This paper discusses the difficulties in modeling, step by step with representative schemes of multisecondary transformer, and advantages/disadvantages of each scheme with simulation results. Finally, a model using flux-coupled cores as basic building blocks is proposed; this model is able to simulate actual transformers very close to its observed parameters in test and actual usage. © 2012 IEEE.

An inductive energy storage pulse power system is being developed in BARC, India. Simple, compact, and robust opening switches, capable of generating hundreds of kV, are key elements in the development of inductive energy storage pulsed power sources. It employs an inductive energy storage and opening switch power conditioning techniques with high energy density capacitors as the primary energy store. The energy stored in the capacitor bank is transferred to an air cored storage inductor in 5.5 μs through wire fuses. By optimizing the exploding wire parameters, a compact, robust, high voltage pulse power system, capable of generating reproducibly 240 kV, is developed. This paper presents the full details of the system along with the experimental data. © 2012 American Institute of Physics.

The KALI-5000 pulse power system was utilized to generate high-power microwaves using a coaxial virtual cathode oscillator. The typical electron-beam parameters were 290 kV, 23 kA, and 100 ns, with a few hundreds of amperes per centimeter square current density. Experiments were conducted using a graphite cathode for two different radial anode-cathode gap distances to investigate the dependence of microwave output magnetic field and frequency on diode voltage and current waveform. It was found that the coaxial vircator always has more than one frequency component. It was shown that the microwave B-field and the frequency do not depend on the time-varying impedance and perveance of the diode. Electron-beam emission area, uniformity, and the anode-cathode gap play a major role in deciding the power density and frequency at the point of measurement. The highest microwave power is emitted when all the power is delivered into a single frequency at least for a certain time of the accelerating pulse. © 2012 IEEE.

The digital pulse processing techniques for high resolution amplitude measurement of radiation detector pulse is an effective replacement of expensive and bulky analog processing as the digital domain offers higher channel density and at the same time it is cheaper. We have demonstrated a prototype digital setup with highspeed sampling ADC with sampling frequency of 80-125 MHz followed by series of IIR filters for pulse shaping in a trigger-less acquisition mode. The IIR filters, peak detection algorithm and the data write-out logic was written on VHDL and implemented on FPGA. We used CAMAC as the read out platform. In conjunction with the full hardware implementation we also used a mixedplatform with VME digitizer card with raw-sample read out using C code. The rationale behind this mixed platform is to test out various filter algorithms quickly on C and also to benchmark the performance of the chip level ADCs against the standard commercial digitizer in terms of noise or resolution. The paper describes implementation of both the methods with performance obtained in both the methods. © 2012 by the respective authors.

The beam from K130 room temperature cyclotron is being extensively used for nuclear physics experiments for last three decades. The typical beam energy for the experiments is approximately 7-10MeV/nucleon for heavy ions and 8-20MeV/nucleon for light ions. The number of detectors used, may vary from one channel to few hundreds of detector channels. The proposed detector system for experiments with the superconducting cyclotron may have more than 1200 detector channels, and may be generating more than one million parameters per second. The VME (Versa Module Europa) and CAMAC (Computer Automated Measurement and Control) based data acquisition system (DAQ) is being used to cater the experimental needs. The current system has been designed based on various commercially available modules in NIM (Nuclear Instrumentation Module), CAMAC and VME form factor. This type of setup becomes very complicated to maintain for large number of detectors. Alternatively, the distributed DAQ system based on embedded technology is proposed. The traditional analog processing may be replaced by digital filters based FPGA (Field Programmable Gate Array) boards. This paper describes the design of current DAQsystem and the status of the proposed scheme for distributed DAQ system with capability of handling heterogeneous detector systems. © 2012 by the respective authors.

A numerical model employing FDTD based particle-in-cell code (PIC) is used to study the discharge mechanism across a gas/solid interface. The simulation is carried out with and without an insulator in the anode cathode gap at a pressure of 1atmosphere and a ramp voltage with a rise time of 5ns and pulse duration of 50ns is used as the input pulse. The profiles of electron densities, avalanche growth, phase profile of electrons, and the gap voltage are calculated with and without an insulator to study the mechanism of discharge in presence of an insulator. Spacer efficiency of 81%is obtained which closely agrees with the existing experimental data.

A Flash X-ray diode has been designed and developed for generation of single shot, nanosecond duration x-rays from KALI-5000 Pulse Power System (0.8-1 MV, 40 kA, 100 ns). The typical electron beam parameter was 500 kV, 8 kA, 100 ns, with a few hundreds of A/cm current density. The spot size for different diode configurations varied from 4 mm to 2 mm. X-ray radiograph of various metal objects were taken on X-ray films. The diode voltage and current waveforms were analyzed with the space-charge limited flow model. The anode and cathode plasma expansion velocities were calculated using the perveance data and varies from 2.5-3.3 cm/μs. Time integrated x-ray dose was measured using pen dosemeter and the on-axis dose was 10 mR at 1m distance from the window. The radiograph of stainless steel objects shows good resolution. © 2011 IEEE.

The most fundamental issues in virtual cathode oscillator (vircator)-based high-power microwave devices are efficiency improvement and oscillation frequency control. We present a study of the time-dependent behavior of the oscillation frequency of a reflex-triode vircator for various anodecathode (AK) gaps. The typical electron-beam parameters were 200 kV, 4 kA, and 300 ns, with a current density of a few hundreds of amperes per square centimeter. Time-dependent frequency analysis is applied to the output signal of the vircator to investigate the time evolution of the emitted frequency spectrum for various AK gaps. We find that the dominant frequency peak is less affected by shot-to-shot fluctuations of diode voltage and current than the other frequency components. In addition, the time of occurrence of the dominant and secondary frequency peaks varies on a shot-to-shot basis. The highest microwave power is emitted when all the power is delivered into a single frequency with minimal mode hopping. © 2006 IEEE.

This paper presents the design and development of a repetitive Marx generator rated at 1 kJ, 300 kV, 12 kA, and 10 Hz and which is suitable to drive the load directly. Bipolar charging of a Marx generator scheme has been adopted to get the following: 1) faster rise time and 2) relatively low charging voltage. The faster rise time is due to the reduced number of spark gaps down to six for 12 in-series capacitors (0.15 μF and 50 kV) of a six-stage bipolar-charging Marx generator. Interstage inductive charging further enhances the efficiency of the overall system as compared to resistive charging. The generator is characterized by an aqueous resistive load for both polarities at the output voltage. Output voltages of the same magnitude have been achieved for both polarities. The matched impedance is found to be 25 Ω for which a suitable reflex triode is designed. Intense electron beams and high-power microwaves have been generated using this Marx generator and reflex triode system. Experimental results demonstrating the Marx generator and the reflex triode operation are presented and discussed. © 2011 IEEE.

Experiments were carried out to generate intense relativistic electron beams and High Power Microwaves (HPM) with reflex triode geometry from 1 kJ pulse power system. The typical electron beam parameters were 300 kV, 12 kA, and 300 ns, with a current density of a few hundreds of amperes per square centimeter. We present a power optimization study of the HPM generated from the reflex-triode vircator for various anode-cathode (AK) gaps. A horn antenna setup with diode detector and attenuators was used to measure the microwave power. The HPM frequency was measured with a D-dot probe along with a high band width oscilloscope. It was found that the microwave power and E-field peaks at 15 mm AK Gap and the frequency at this gap is 2.2 GHz. The highest microwave power is emitted when all the power is delivered into a single frequency with minimal mode hopping. © 2011 IEEE.

Linear Induction accelerator rated 200kV, 5kA, 100ns and 100Hz repetition rate has been designed and developed in the division. Electron linear induction accelerator belongs to a new class of short pulse, high average power accelerator being developed for various industrial, medical and defense application. The satisfactory performance of all the sub-systems including solid state power modulator, amorphous core based pulse transformers, magnetic switches, water capacitors; water pulse-forming line, voltage induction cavity in adder mode (IVA) and explosive emission electron diode have been demonstrated. This paper mainly focuses on schematic, operation and operational results of induction voltage adder of LIA-200. © 2011 IEEE.

This paper presents the work being conducted in our laboratory on direct driving of HPM load using opening switch consisting of electrically exploding wire array. Using the opening switch, desired voltage profile required for driving the load has been achieved and HPM has been generated along with making the complete system compact and portable which otherwise is difficult to envisage. © 2011 IEEE.

This paper presents a new high voltage pulse shaping methodology for pulsed power applications. The aim is to generate high voltage square pulse across anode cathode gap of e-beam diodes. The non-linear time varying perveance characteristics of e-beam diodes are used for shaping of output voltage pulse across it, generated directly from Marx generator. Analytically, it has been shown in the paper that under certain conditions, if achieved, Marx generator feeding an e-beam diode can produce a square-like pulse at the output, without any extra pulse shaping arrangements. Experimental results to support the analysis are also presented in the paper. © 2011 American Institute of Physics.

The research results of the explosive field emission cathode plasma expansion velocity and the initial emission area in the planar diode configuration with cathodes made of graphite, stainless steel, polymer velvet, carbon coated, and carbon fiber (needle type) cathodes are presented. The experiments have been performed at the electron accelerator LIA-200 (200 kV, 100 ns, and 4 kA). The diode voltage has been varied from 28-225 kV, whereas the current density has been varied from 86-928 Acm2 with 100 ns pulse duration. The experimentally obtained electron beam diode perveance has been compared with the 1 dimensional Child-Langmuir- law. It was found that initially only a part of the cathode take part in the emission process. The plasma expands at 1.7-5.2 cmμ/s for 4 mm anode-cathode gap for various cathode materials. It was found that the plasma expansion velocity increases with the decrease in the cathode diameter. At the beginning of the accelerating pulse, the entire cathode area participates in the electron emission process only for the multiple needle type carbon fiber cathode. © 2011 American Institute of Physics.

Pulse Step Modulation based High voltage power supply has played significant role in fusion research. Multi-Secondary transformers are invariably used for generation of tens of kV range outputs with fast (μS order) transient response. In this scheme, large numbers of isolated voltage sources are connected in series to generate the output. Isolated voltage sources can be achieved by large number of separate transformers or by single unit of multi-secondary transformer. Naturally, a transformer having numbers of secondary windings (∼40) on single core is the preferred solution due to its space and cost consideration. For design and simulation analysis of such a power supply, the model of a multi-secondary transformer poses special problem to any circuit analysis software. While many simulation softwares provide transformer models with limited number (3-6) of secondary windings, they still fail to predict the actual observed results from a manufactured unit. This paper discusses the difficulties in modelling, step by step with representative schemes of multi-secondary transformer, advantages/disadvantages of each scheme with simulation results. Finally, a model using flux coupled cores as basic building block is proposed, this model is able to simulate actual transformers very close to its observed parameters in test and actual usage. © 2011 IEEE.

Experiments were carried out to generate High Power Microwaves (HPM) from KALI 5000 pulse power system using an axial and a coaxial virtual cathode oscillator (vircator). The KALI 5000 pulse power system is a Marx generator and Blumlein line based system capable of operation at 1 MV, 50 kA, 100 ns. The typical electron beam parameters were 400 kV, 20 kA, and 100 ns, with a current density of a few hundreds of amperes per square centimeter. It was found that the generated HPM power is almost negligible in an axial vircator configuration due to severe impedance collapse problem. Impedance collapse in a planar diode due to fast cathode and anode plasma expansion and bipolar flow across the diode gap. However, HPM could be generated in a coaxial vircator configuration because of the fact that the electrode plasma expansion velocity of the cylindrical diode is much smaller as compared with the planar diode for the same accelerating gap and diode voltage. Therefore, much higher voltage can be obtained for the cylindrical diodes as compared with the planar diodes for the same accelerating gap. The measured HPM power density and the electric field strength at antenna mouth are (4.3 m distance from the Vircator window) 104.5 kW/m 2 and 6.27 kV/m respectively. Frequency of the HPM signal was 2.9 GHz and a time-dependent frequency analysis shows that the frequency remains constant in time for almost entire pulse duration. © 2011 IEEE.

Experiments were carried out to generate intense relativistic electron beams and High Power Microwaves (HPM) with reflex triode geometry from 1 kJ pulse power system. The 1 kJ pulse power system is a Marx generator based repetitive system capable of operation at 10 Hz. The typical electron beam parameters were 200 kV, 4 kA, and 300 ns, with a current density of a few hundreds of amperes per square centimeter. The cathode used was planar graphite and the anode is a woven stainless steel mesh of 70% transparency. Beam generation studies were conducted for diode gaps from 8-20 mm. Cathode plasma expansion velocity has been calculated from the time dependent diode perveance and was found to be 1.7 cm/μs. It was also found that the microwave (base not FWHM) pulse width increased from ∼ 150 ns to ∼ 700 ns as the diode gap is increased from 8 mm to 20 mm. A large pulse width is obtained because of longer time of plasma motion across the gap and reduced rate of the effective gap change. Measured frequency was 2.2 GHz at 15 mm anode-cathode gap and decreases with the increased gap. © 2011 IEEE.

Rogowski coils have been used for decades for non-invasive current measurement when other probe, such as current shunts, current transformers are impracticable. The measurement of diode beam current in pulse power system under vacuum and high voltage are challenging task which requires development of Rogowski coil for specific applications. They operate in large radiation fields, under intense electron bombardment and at high di/dt. The Rogowski coil has been developed and calibrated to detect nano second pulsed currents from 10kA to 100kA with wide bandwidth and sensitivity. This paper describes Calibration of Rogowski coil used for measuring KALI-1000 pulsed power system[1] relativistic electron beam current. Rogowski coi designed and fabricated using damping resistor technique is also described. © 2011 IEEE.

Intense electron beam generation studies were carried out using polymer velvet as a cathode material. The typical electron beam parameters were 250 kV, 15 kA, 100 ns, with a few hundred A cm-2 current density. The cathode plasma expansion velocity and the effective initial emission area have been calculated using the perveance data. It was found that the gap closure velocity and the initial emission areas vary randomly on a shot-to-shot basis. In comparison with a graphite cathode, the gap closure velocity of the velvet cathode is less for lower diode gaps, but is much higher for the larger accelerating gaps. One-way analysis of variance was employed to examine the statistical correlation between the diode voltage, current, plasma velocity and the effective emission area for various diode gaps and for two different cathode materials. It was shown that the mean diode voltage, current, plasma velocity and the effective emission area are different for graphite and velvet cathodes whereas the statistical variations of diode voltage and plasma expansion velocities are not cathode material dependent. However, the mean effective emission area is cathode material dependent as are the variances. © 2010 IOP Publishing Ltd.

The KALI-1000 pulse power system has been used to generate single-pulse nanosecond-duration high-power microwaves from an axial virtual cathode oscillator. The typical electron beam parameters were 250 kV, 15 kA, and 100 ns, with a current density of a few hundreds of amperes per square centimeter. The shot-to-shot variation of the microwave pulsewidth was studied for various anodecathode gaps and two different cathode materials (velvet and graphite). Results indicated that the average microwave pulsewidth for a diode with a graphite cathode increased as the anodecathode gap was increased. The one-way analysis of variance was employed to examine the statistical correlation between the diode voltage, current, perveance, and the microwave pulsewidth for various diode gaps and for two different cathode materials. It was shown that the microwave pulsewidth variations are not statistically correlated with the diode voltage, current, and perveance. © 2006 IEEE.

Repetitive Pulsed Power Technology is being developed keeping in mind the potential applications of this technology in material modifications, disinfections of water, timber, and food pasteurization etc. BARC has indigenously developed a Linear Induction Accelerator (LIA-200) rated for 200 kV, 4 kA, 100 ns, 10 Hz. The satisfactory performance of all the sub-systems including solid state power modulator, amorphous core based pulsed transformers, magnetic switches, water capacitors, water pulse- forming line, induction adder and field-emission diode have been demonstrated. This paper presents some design details and operational results of this pulsed power system. It also highlights the need for further research and development to build reliable and economic high-average power systems for industrial applications. © 2010 IOP Publishing Ltd and SISSA.

High power microwave (HPM) generation studies were carried out in KALI-5000 pulse power system. The intense relativistic electron beam was utilized to generate HPMs using a coaxial virtual cathode oscillator. The typical electron beam parameters were 350 kV, 25 kA, and 100 ns, with a few hundreds of ampere per centimeter square current density. Microwaves were generated with graphite and polymer velvet cathode at various diode voltage, current, and accelerating gaps. A horn antenna setup with diode detector and attenuators was used to measure the microwave power. It was observed that the microwave power increases with the diode voltage and current and reduces with the accelerating gap. It was found that both the peak power and width of the microwave pulse is larger for the velvet cathode compared to the graphite cathode. In a coaxial vircator, velvet cathode is superior to the graphite cathode due to its shorter turn on time and better electron beam uniformity. © 2010 American Institute of Physics.

Intense electron beam generation studies were carried out in high power cylindrical diode to investigate the effect of the accelerating gap and diode voltage on the electron beam current. The diode voltage has been varied from 130 to 356 kV, whereas the current density has been varied from 87 to 391 A/ cm2 with 100 ns pulse duration. The experimentally obtained electron beam current in the cylindrical diode has been compared with the Langmuir-Blodgett law. It was found that the diode current can be explained by a model of anode and cathode plasma expanding toward each other. However, the diode voltage and current do not follow the bipolar space-charge limited flow model. It was also found that initially only a part of the cathode take part in the emission process. The plasma expands at 4.2 cm/μs for 1.7 cm anode-cathode gap and the plasma velocity decreases for smaller gaps. The electrode plasma expansion velocity of the cylindrical diode is much smaller as compared with the planar diode for the same accelerating gap and diode voltage. Therefore, much higher voltage can be obtained for the cylindrical diodes as compared with the planar diodes for the same accelerating gap. © 2010 American Institute of Physics.

KALI-1000 pulse power system has been used to generate single pulse nanosecond duration high-power microwaves (HPM) from a virtual cathode oscillator (VIRCATOR) device. HPM power measurements were carried out using a transmitting-receiving system in the presence of intense high frequency (a few MHz) electromagnetic noise. Initially, the diode detector output signal could not be recorded due to the high noise level persisting in the ambiance. It was found that the HPM pulse can be successfully detected using wide band antenna, RF cable and diode detector set-up in the presence of significant electromagnetic noise. Estimated microwave peak power was ̃59.8 dBm (̃1 kW) at 7 m distance from the VIRCATOR window. Peak amplitude of the HPM signal varies on shot-to-shot basis. Duration of the HPM pulse (FWHM) also varies from 52 ns to 94 ns for different shots. © Indian Academy of Sciences.

Intense gigawatt relativistic electron beam generation studies were carried out with a Perspex cathode holder. Purpose of the dielectric cathode holder was to minimize the prepulse voltage across the diode. The typical electron beam parameter was 180 kV, 26 kA, 100 ns, with a few hundreds of ampere per square centimeter current density. It was found that corrugated Perspex of length ≥ 35 mm can eliminate the prepulse voltage but affects the rise time of the diode voltage. The diode voltage and current waveforms were analyzed with the bipolar space-charge limited flow model. The anode and cathode plasma expansion velocities were calculated using the perveance data. The plasma expands at 5.1 cm/μs for 18-mm anode-cathode gap and the plasma velocity increases for larger gap. Inserting a dielectric at the cathode holder could be a very effective method to reduce prepulse voltage at the electron beam diode, but it increases the rise time of the diode voltage and reduces the effective electron beam pulsewidth. The prepulse voltage reduces significantly (≤ 10%) when an inductance is added to the charging circuit of the Blumlein line. © 2008 IEEE.

The shot to shot variation in perveance of a planar diode with explosive emission graphite cathode in a range of accelerating gaps 3-12 mm is investigated experimentally. The typical electron beam parameters were 200 kV, 12 kA, 100 ns, with a few hundreds of A/ cm2 current density. The diode perveance remains less than the Child-Langmuir value, indicating that only a fraction of the cathode take part in the emission process. A simple statistical analysis of the diode perveance shows that the shot to shot variation is more pronounced for the later part of the accelerating pulse. The cathode plasma expansion velocity and the effective initial emission area have been calculated from the perveance data. It was found that the plasma expansion velocity varies from 3 to 6.5 cm/μs. The mean expansion velocity and the standard deviation increase with the increase in the accelerating gap. The initial emission areas also varies randomly on a shot to shot basis and at the beginning of the accelerating pulse only 4%-35% of the cathode area take part in the emission process. The mean initial emission area and the standard deviation also increase with the increase in the accelerating gap. Experimental result indicates that the larger gaps and lower electric fields suggest a path to more uniform emission. © 2009 American Institute of Physics.

High power electron beam generation studies were carried out in a planar diode configuration to investigate the effect of the accelerating gap, diode voltage, and anode-cathode materials on the electrode plasma expansion. The diode voltage has been varied from 145-428 kV, whereas the current density has been varied from 208-2215 A/ cm2 with 100 ns pulse duration. It was found that the diode voltage and current follow the bipolar space-charge limited flow model. The anode and cathode plasma expansion velocities were calculated using the perveance data. The plasma expands at 11 cm/μs for 34 mm anode-cathode gap and the plasma velocity decreases for smaller gaps. It was found that the plasma expansion velocity increases significantly due to the cathode edge contribution and the edge contribution is particularly important during the beginning and the end of the accelerating pulse when the diode voltage and the corresponding electric field are comparatively low. It was also observed that the diode current increased by a factor of 3 when anode material was released into the accelerating gap due to the electron beam bombardment. © 2009 American Institute of Physics.

A pulse power system (1 MV, 50 kA, and 100 ns) based on Marx generator and Blumlein pulse forming line has been built for generating high power microwaves. The Blumlein configuration poses a prepulse problem and hence the diode gap had to be increased to match the diode impedance to the Blumlein impedance during the main pulse. A simple method to eliminate prepulse voltage using a vacuum sparkgap and a resistor is given. Another fundamental approach of increasing the inductance of Marx generator to minimize the prepulse voltage is also presented. Experimental results for both of these configurations are given. © 2009 American Institute of Physics.

A single cell 1050 MHz, β = 0.49 elliptical cavity has been designed for possible use in High Current Proton Accelerator. The structural behavior of the single cell superconducting elliptical cavity has been studied by finite element structural analysis code. The max. Von MISES stress and cavity wall displacements were calculated under the vacuum load for various wall thickness. Both niobium and copper have been considered as cavity material. The RF resonant frequency shift due to the static Lorentz force has been calculated for 3 mm wall thickness. Structural properties of the 1050 MHz, β = 0.49 cavity have been compared with the 700 MHz, β = 0.42 single cell elliptical cavity. It was found that from structural point of view 1050 MHz, β = 0.49 cavity is more suitable for high current proton accelerator. © 2008 IOP Publishing Ltd and SISSA.

A pulse power system (1MV, 50kA, and 100ns) based on dual polarity charged Marx generator and Blumlein pulse forming line (PFL) was built to generate high power microwaves. This paper describes the inherent prepulse present with the Blumlein configuration and the mitigation strategies adopted. Further, a qualitative attempt to verify the generation of high power microwave output on the system is presented. © 2008 IEEE.

Flash x-ray generation studies have been carried out in KALI-5000 Pulse power system. The intense relativistic electron beam has been bombarded on a tantalum target at anode to produce flash x-ray via bremsstrahlung conversion. The typical electron beam parameter was 360 kV, 18 kA, and 100 ns, with a few hundreds of A/ cm2 current density. The x-ray dose has been measured with calcium sulfate:dysposium (CaSO4:Dy) thermoluminescent dosimeter and the axial dose distribution has been characterized. It has been observed that the on axis dose falls of with distance ∼1/ xn, where n varies from 1.8 to 1.85. A maximum on axis dose of 46 mrad has been measured at 1 m distance from the source. A plastic scintillator with optical fiber coupled to a photomultiplier tube has been developed to measure the x-ray pulse width. The typical x-ray pulse width varied from 50 to 80 ns. © 2008 American Institute of Physics.

A comparison of various thermometric techniques used for the estimation of nuclear temperature has been made from the decay of hot composite 32S* produced in the reaction 20N(145MeV)+12C. It is shown that the temperatures estimated by different techniques, known to vary significantly in the Fermi energy domain, are consistent with each other within experimental limits for the system studied here. © 2008 The American Physical Society.

Intense relativistic electron beam generation studies were carried out in a planar diode configuration to investigate the effect of the plasma expansion on the impedance characteristics of the diode. The typical electron beam parameter was 280 kV, 18 kA, 100 ns, with a few hundreds of A cm2 current density. The diode voltage and current waveforms were analyzed with the bipolar space-charge limited flow model. The anode and cathode plasma expansion velocities were calculated using the perveance data. The plasma expands at 9.5 cmμs for 31 mm anode-cathode gap and the plasma velocity decreases for smaller gap. It was found that the electron emission is more uniform for 25 mm anode-cathode gap as compared to 31 mm gap. Effect of a nylon sheet on the anode plate has been studied with respect to the impedance characteristic of the diode. It was found that the diode closes at a faster rate in the presence of nylon sheet on anode. Nylon materials are released into the diode region due to the electron beam bombardment and get deposited on the cathode. This deposition affects the subsequent electron beam generation. © 2008 American Institute of Physics.

Intense gigawatt relativistic electron beam generation studies were carried out in the presence of prepulse. Electron beams were generated using planar and annular graphite cathodes of various diameters at a fixed 25 mm anode-cathode gap. For the planar cathode, the beam parameters obtained are 340 keV, 24 kA, and 100 ns at a 680 A cm2 current density. With an annular cathode, 346 keV, 10 kA, and 100 ns electron beam could be generated at a 3.4 kA cm2 current density. The peak electric field in the diode varies from 58 to 138 kVcm. A bipolar prepulse voltage has been recorded at the diode for both the cathodes. The amplitude of the negative prepulse voltage varies with the Marx generator voltage but the time duration remains same. The positive prepulse voltage varies both in amplitude and time duration with the Marx generator voltage. Some shot to shot variation in the diode voltage and current were recorded for the annular cathode due to the nonreproducibility of the prepulse generated plasma. It was found that the effect of prepulse is more pronounced in the cathode of larger diameter. © 2008 American Institute of Physics.

Our previously reported results demonstrated that an intense gigawatt relativistic electron beam can be generated in a cylindrical diode in the presence of prepulse. This article reports intense electron beam generation in a cylindrical electron beam diode when subjected to a high voltage bipolar pulse. The experimental results are compared to the Langmuir-Blodgett law. The diode perveance in the positive voltage pulse linearly increases with time due to the increase in the emission area. It was found that the electron beam can be generated from the diode during the negative voltage pulse due to a very little gap closure during the positive voltage pulse. © 2008 American Institute of Physics.

Intense gigawatt relativistic electron beam has been generated in a high power cylindrical diode in the presence of prepulse. A bipolar prepulse voltage, recorded at the diode, varies both in amplitude and time duration with the Marx generator voltage. It was found that only at the accelerating gap ≤1.65 cm there is some shot to shot variation in the diode voltage and current for the same Marx generator voltage. The anode and cathode plasma expansion velocities were calculated using the perveance data. The plasma expands at 5 cmμs for 1.85 cm radial anode-cathode gap and the plasma velocity decreases for smaller gap. It was found that the effect of the prepulse is less pronounced in the cylindrical diode as compared to planar diode that allows one operation of the cylindrical diode with the gap ≤1.85 cm. © 2008 American Institute of Physics.

BARC is developing technology for the accelerator driven subcritical system (ADSS) that will be mainly utilized for the transmutation of nuclear waste and enrichment of U233. Design and development of superconducting medium velocity cavity has been taken up as a part of the accelerator driven subcritical system project. We have studied RF properties of 1050 MHz, β = 0.49 single cell Elliptical cavity for possible use in High Current Proton Accelerator. Cavity shape optimization studies have been done by means of 2D cavity tuning code SUPERFISH and 3D High Frequency Simulation code CST Microwave Studio. The cavity peak electric and magnetic fields, power dissipation P c, quality factor Q and effective shunt impedante ZT2 were calculated for various cavity dimensions using these codes. Based on these analyses a list of design parameter for the inner cell of the cavity has been suggested for possible use in high current proton accelerator. © 2008 IOP Publishing Ltd and SISSA.

BARC is developing a technology for the accelerator-driven subcritical system (ADSS) that will be mainly utilized for the transmutation of nuclear waste and enrichment of U233. Design and development of superconducting medium velocity cavity has been taken up as a part of the accelerator-driven subcritical system project. We have studied RF properties of 700 MHz, β= 0.42 single cell elliptical cavity for possible use in high current proton acceleration. The cavity shape optimization studies have been done using SUPERFISH code. A calculation has been done to find out the velocity range over which this cavity can accelerate protons efficiently and to select the number of cells/cavity. The cavity's peak electric and magnetic fields, power dissipation Pc, quality factor Q and effective shunt impedance ZT2 were calculated for various cavity dimensions using these codes. Based on these analyses a list of design parameters for the inner cell of the cavity has been suggested for possible use in high current proton accelerator. © Indian Academy of Sciences.

A pulse power system (1 MV, 50 kA, and 100 ns) based on Marx generator and Blumlein pulse forming line has been studied for characterization of a general system. Total erected Marx inductance and series resistance are calculated from modular testing of Marx generator and testing of Marx generator with Blumlein. The complete pulse power system has been tested with the termination of a liquid resistor load for finding the Blumlein characteristic impedance. Equivalent electrical circuits during the charging and discharging of the Blumlein are constructed from the characterized parameters of the system. These equivalent circuits can be used in the analysis of prepulse voltage and droop in the flat top of the main pulse in the pulse power systems based on Marx generator and Blumlein. © 2007 American Institute of Physics.

Intense relativistic electron beam diode has been operated without a prepulse switch. Our previously reported results demonstrated that the large pulse power systems in the presence of prepulse can deliver gigawatt power pulses into a matched load if the anode cathode gap is set larger than that estimated by the Child Langmuir relation. This article reports some more experimental results on the current and voltage characteristics, the shot to shot reproducibility of the diode in the presence of prepulse. Intense electron beam diode behavior was studied for various anode cathode gaps and voltages in presence of prepulse. It has been observed that for small gap, prepulse generated plasma completely fills the anode cathode gap and the diode behaves as plasma filled diode. At a large gap the beam parameters obtained are 420 keV, 22 kA, 100 ns. From the experimentally obtained values of perveance an upper limit was set up for the Marx voltage (or anode cathode voltage) and lower limit for the anode cathode gap in order to avoid the gap closure problem and the diode can be operated with a better shot to shot reproducibility. © 2007 American Institute of Physics.

Large pulse power systems in the presence of prepulse can deliver gigawatt power pulses into a matched load. While employing these pulse power systems for the generation of intense relativistic electron beams (IREBs), the prepulse initiated plasma closes the anode cathode gap, if the gap distance is set by the Child-Langmuir formula. In order to reduce the prepulse effect, the anode cathode gap has been increased for the generation of IREB with output parameters of 400 kV, 20 kA, and 100 ns pulse duration. In this paper the generation of IREB in the presence of prepulse without using any prepulse switch has been discussed. © 2007 American Institute of Physics.

High power microwave (HPM) radiation with frequency>1 GHz may penetrate electronic systems through front or backdoor openings and propagate like the genuine signal. Sometimes parasitic resonance may amplify the HPM signal and cause havoc to these systems. The surface currents caused by HPM can also interfere with the normal signals and upset the functioning of devices. The HPM incident upon electronic components may damage them through mechanisms like adiabatic heating of the junction or punch-through of the depletion layer. High power microwave radiation generation studies were performed using the intense electron beam from the KALI-1000 Pulse Accelerator by the virtual cathode oscillator method. Various axial resonant cavities were used to optimise the microwave emission. A maximum power of 500 MW around 5 GHz was generated by using an axial resonant cavity with a resonant frequency of 5 GHz. The HPM was also used to study the effects on some electronic devices. The HPM caused damage to the op-amps and stopped the functioning of the personal computers. The HPM can also cause breakdown in the low-pressure devices like hydrogen thyratrons and cause spurious triggering in the control circuits that use them.