Electromagnetic Shock Tube Research Articles

Analytical and numerical modeling of high-strain rate metal-tube forming

In this research, a novel plasto-dynamic analytical and numerical modeling is developed for tube expansion during a high-strain rate forming process, such as electromagnetic and liquid shock tube forming. The analytical model is based on applying the impact mechanic and shell theories with introducing an effective load along with imposing high-order non-linearity of material behavior. The numerical model is also conducted by dynamic explicit finite element setup with considering an equivalent transient and traveling load. Both analytical and numerical models are compared ‌with each other and validated with experimental measurements of different processes available in literature. The analytical model has satisfactorily acceptable prediction, especially for small strains, locations far from dies or supports, and for processes with high load-to-material resistance ratio and with less complicated interaction and loading nature. The numerical modeling is also effective if precise data input is provided. Several parameter studies are carried out, and conditions for achieving a high-performance forming process are discussed. The magnitude of total impulse and inertia force have significant roles, but traveling speed and profile shape of load have no considerable effects on plastic deformation. For AISI 316L, strain hardening and thermal softening have major and minor influences on material strength, respectively.

The reflection of an ionized shock wave

In a previous paper we studied the thermodynamic and kinetic theory for an ionized gas, in one space dimension; in this paper we provide an application of those results to the reflection of a shock wave in an electromagnetic shock tube. Under some reasonable limitations, which fully agree with experimental data, we prove that both the incident and the reflected shock waves satisfy the Lax entropy conditions; this result holds even outside genuinely nonlinear regions, which are present in the model. We show that the temperature increases in a significant way behind the incident shock front but the degree of ionization does not undergo a similar growth. On the contrary, the degree of ionization increases substantially behind the reflected shock front. We explain these phenomena by means of the concavity of the Hugoniot loci. Therefore, our results not only fit perfectly but explain what was remarked in experiments.

Dynamics of quasi-empty rupture in the layer of cavitating liquid under SW-loading

The problem of formation and collapse of a quasi-empty rupture in the layer of a cavitating liquid under shock wave (SW) loading is considered. The SW-pulse is generated in the layer by electro-magnetic hydrodynamic shock tube in a result of high-voltage discharge of capacitor bank on a flat helical coil. The latter is located right up to the bottom (conducting membrane) of container with the layer of two-phase distilled liquid. The analysis of the experimental data shows that the rupture is shaped as a spherical segment, which retains its topology during the entire process of its evolution and collapse. It was shown that potential energy of maximum volume of rupture at its collapse is practically transformed in acoustical losses (SW-radiation) and rupture disappears. Dynamics of main parameters and an existence time of rupture were determined. The analysis of cavitating nuclei state in the form of thin layer on an entire interface of rupture shows that in the field of rupture collapse the thin cavitating layer is transformed to a cavitating cluster. The latter takes the form of a ring-shaped bubbly vortex floating upward to the free surface of the liquid layer. A р-к two-phase mathematical model was formulated, and calculations were performed to investigate the collapse of a quasi-empty spherical cavity (rupture model) in the unbounded cavitating liquid, generation of ultra-short shock wave and to discover the dynamic growth of micro-bubbles in a cluster by five orders of magnitude. [Work supported by RFBR Grant 15-05-03336.]

Formation of a cavitation cluster in the vicinity of a quasi-empty rupture

The presentation deals with one of the experimental and numerical models of a quasi-empty rupture in the magma melt. This rupture is formed in the liquid layer of a distilled cavitating fluid under shock loading within the framework of the problem formulation with a small electromagnetic hydrodynamic shock tube. It is demonstrated that the rupture is shaped as a spherical segment, which retains its topology during the entire process of its evolution and collapsing. The dynamic behavior of the quasi-empty rupture is analyzed, and the growth of cavitating nuclei in the form of the boundary layer near the entire rupture interface is found. It is shown that rupture implosion is accompanied by the transformation of the bubble boundary layer to a cavitating cluster, which takes the form of a ring-shaped vortex floating upward to the free surface of the liquid layer. A p-κ mathematical model is formulated, and calculations are performed to investigate the implosion of a quasi-empty spherical cavity in the cavitating liquid, generation of a shock wave by this cavity, and dynamics of the bubble density growth in the cavitating cluster by five orders of magnitude.

On the mechanism of explosive eruption of mount erebus volcano: the dynamics of the rupture structure in a cavitating layer

This paper presents the results of an experimental simulation of rupture development in heavily cavitating magma melt flow in volcanic conduits and its effect on the structure of explosive volcanic eruptions. The dynamics of the state of a layer of distilled water (similar in the density of cavitation nuclei to magma melt) under shock-wave loading was studied. The experiments were performed using electromagnetic hydrodynamic shock tubes (EM HST) with maximum capacitor bank energy of up to 100 J and 5 kJ. It was found that the topology of the rupture formed on the membrane surface did not change during its development. Empirical estimates were obtained for the proportion of the capacitor bank energy expended in the development of the rupture and the characteristic time of its existence. The study revealed a number of fundamentally new physical effects in the cavity dynamics in a cavitating medium: a cavitation “boundary layer” is formed on the surface of the quasi-empty rupture, which is transformed into a cluster of high energy density upon closure of the flow.

Velocity evolution of electro-magnetically driven shock wave for beam-dissociated hydrogen interaction experiment

We present the velocity measurements in electro-magnetic shock tube for beam interaction experiment by three methods; laser refraction, photodiode for self-emission, and high speed framing camera. The laser refraction showed that the average shock velocity was 6.7 km/s when the initial pressure was 1000 Pa and the initial charging voltage was 16 kV. The self-emissions from piston discharge plasma were measured by photodiodes and by high speed framing camera. The measurements showed that the duration between shock and piston was up to 8 microseconds with a 400-mm propagation in the shock tube, which is enough time as dissociation target for beam interaction experiment.The complementary velocity measurement is significant for understanding the electro-magnetically driven shock physics.

Well-defined atomic hydrogen target driven by electromagnetic shock wave for stopping power measurement

AbstractThe precise estimation of stopping power is crucial to predict the beam energy loss in the target for heavy-ion fusion and heavy-ion-driven high-energy density physics experiments. The electromagnetic shock wave has been proposed to generate a well-defined atomic hydrogen target for the stopping power measurement with dissociation effects. We measured the angular distribution profile of the discharge plasma and the plasma velocity in the electromagnetic shock tube by high-speed framing cameras. To improve the uniformity of the discharge plasma and the velocity, an external magnetic field was applied in the electromagnetic shock tube. The plasma velocity was up to approximately 40 km/s for an initial hydrogen gas pressure of 100 Pa and the velocity decreased with the initial pressure and the propagation length. The framing cameras showed that angular distributions of the discharge plasmas were not uniform and the initial angular distributions were important for the development of plasma profiles. The interaction of the plasma with the external magnetic field was estimated using the ratio of the plasma dynamic pressure to the magnetic pressure. The estimations offer more magnetic fields to improve the discharge uniformity due to the interaction.

Velocity Measurement of Electromagnetically-driven Shock Wave to Produce a Dissociated Hydrogen Target for Beam Interaction Experiment

Abstract Heavy ion fusion sciences and heavy-ion-driven high energy density physics experiments require evaluations of the stopping power with dependences on target density and temperature. We are interested in effects of dissociation of the target molecules which have not been experimentally investigated. The electro-magnetically driven shock wave has been proposed to produce well-defined dissociated target which is required to measure the stopping power with the dissociated effect. We have velocity measurements in the electro-magnetic shock tube to understand the target physical condition. The velocity measurement by laser refraction gives reliable experimental results, which shows that the shock velocity is not enough to dissociate hydrogen completely. The experiments indicate that input energy does not convert to the piston plasma in electro-magnetic shock tube efficiently.

Electro-magnetically driven shock and dissociated hydrogen target for stopping power measurement

A design study of electro-magnetic shock tube for dissociated gas targets is presented. Behind the shock front, there is a dissociated gas region without ionization. That is suitable target for the stopping power measurement when we have an appropriate shock velocity. The previous experiments showed that the dissociated target duration with uniform density and temperature profiles as long as microsecond was required for synchronization with projectile. A new shock tube with long drift section is proposed. The duration of shock heated region can be estimated to be 2μs in this design. This configuration enables us to measure the difference of the stopping power between molecules and dissociated atoms for heavy ion beams more reliably.

Development of a coaxial tapered electromagnetic shock tube for beam–plasma non-linear interaction experiments

A coaxial electromagnetic shock tube was developed to produce a non-ideal plasma target with Γ∼0.1 (Γ: Plasma coupling constant) for non-linear interaction experiments between ion beams and plasmas. To evaluate the shock velocity, we photographed the trajectory of the shock front along the tube by a streak camera. From these measurements, we found that the shock waves are strong enough to produce a non-ideal plasma in the tube. To reduce the plasma thickness for the stopping power measurements, the effective diameter of the tube was reduced by using a tapered section. The effects of the tapered section on the shock velocity and the shape of the shock front were examined. Using a 30 tapered section, the shock velocity was increased up to 54km/s compared with 47km/s for a straight tube.

Development of a non-ideal plasma target for non-linear beam–plasma interaction experiments

A shock-driven plasma target was developed to examine non-linear interactions between low-energy heavy ions and cold-dense plasmas. MD calculations predicted that beam–plasma coupling constant γ ∼ 0.1 must be achieved to observe the non-linearity, which corresponds to the plasma coupling constant Γ ≈ 0.2 for projectiles of v proj ≈ 10 keV / u and q ≈ 2 . One-dimensional numerical estimations using SESAME equation of state showed that a shock wave propagating in 5-Torr H 2 gas with 47 km/s must be produced to satisfy Γ ≈ 0.2 . Utilizing an electromagnetic shock tube with a peak current of 50 kA and a current rise time of 800 ns, we achieved a shock speed of 45 km/s. The electron density distribution of the shock-produced plasma along the beam axis was measured by a Mach–Zehnder interferometer. From this measurement we confirmed that the electron density was over 10 17 cm - 3 and the homogeneity was acceptable during several hundred nanoseconds. The electron temperature was also determined by optical spectroscopic measurements. The Coulomb coupling constant was evaluated using these experimental data to investigate feasibility of the beam–plasma interaction experiments.

1011 CO_2 レーザヘテロダイン干渉計を用いた衝撃波プラズマの電子密度測定

The temporal variation of electron density of shocked Ar plasma, generated with a T-shaped electromagnetic shock tube, were measured by a CO_2 laser heterodyne interferometer with 20MHz beat signals produced by an acousto-optic modulator. The interference signal is detected by HgCdTe detector. This signal and reference signal from AOM driver were inputted into phase comparator, and outputted cos and sin functions with phase difference between two signals. Then, these were recorded by digital storage oscilloscope, and computed to determined phase difference. As a result, high resolution measurements for fast moving plasma were achieved. And, PIN photodiode array for measured shock speed were used.

Formation of thin films by shock wave deposition method

A T-shaped electromagnetic shock tube was used to deposit thin films of NbN and MoN on fused quartz substrates at room temperature. Deposition of NbN was carried out with Nb as the electrode material, niobium pellets were placed between the electrodes, and the initial pressure was 400 Pa in an N 2H 2 mixture. Examination by XMA and ESCA showed that the thin film is composed mainly of NbN and is 50–60 nm thick. The nitrogen concentration ranged from 10% to 20%. In the case of MoN the thickness was about 50 nm for two plasma shots and 200 nm for eight plasma shots. All of the films exhibited the superconductivity transition.

Asymmetry of the H β central part measured in a T-tube

The asymmetry parameter δ I of the H β central part has been measured as a function of the plasma electron density. The results are compared with recently published theories and measurements. The plasma source was a small electromagnetic T-shaped shock tube. The electron density varied between 0.7 x 10 23 and 3 x 10 23m -3, while the temperatures were 20,000 K and more.

Measurements of the glass-to-plasma boundary-layer influence on continuum radiation in a T-tube

The influence of the glass-to-plasma boundary layers on the continuum radiation of hydrogen plasma has been experimenally checked at the Hβ wavelength by introducing an additional number of boundary layers into the observed plasmas produced inside of a T-shaped electromagnetic shock tube. In the first case (case A), the plasma was observed (by using a monochromator) with the two usual boundary layers. In the second case (case B), four additional boundary layers were created by introducing two glass plates into the plasma. During the first microsecond, after the reflected shock front had passed the point of observation, no major differece was noted between the continuum intensities in cases A and B. At 1.5 μs and later, the difference amounted to about 10 to 20% with case B being more intense, depending on time, that is on the plasma parameters and boundary-layer thickness.

Measurement of Specific Heats Ratio of Hydrogen Plasma

AbstractAdiabatic expansion of plasma behind the reflected shock front in an electromagnetic shock tube has been verified. Electron densities and temperatures have been measured spectroscopically. Assuming complete local thermal equilibrium, the specific heat ratios of hydrogen plasmas have been determined out of expansion rate per a heavy particle directly from the adiabatic expansion law. Noticeably lower values of the ratio are determined at temperatures where ionization and recombination processes are abundant. The ratios determined in this work are in excellent agreement with theoretical values determined in an earlier work.

A measurement of the two-dimensional structure of the flow in a coaxial shock tube

An optical (633 nm) Michelson interferometer in which the length of the reference arm is varied by means of a pair of rotating mirrors, has been used to measure the phase shift produced in the probing beam during the propagation of transverse magnetohydrodynamic and ionizing shock waves in a coaxial electromagnetic shock tube. The measurements, which achieve a phase resolution of about 0.1 rad with a time resolution of 70 nsec, have been obtained at three chordal positions and are inverted by Abel transform to give a coarse picture of the two-dimensional electron density distribution in the tube. This distribution shows marked radial nonuniformity, indicating that 2-D effects are of considerable importance in determining the dynamics and structure of the transverse shock waves produced in a coaxial geometry.

Refractive Q-switching of a ruby laser by a moving plasma

A ruby laser was Q-switched by means of a plasma. The plasma, which had a density of up to 10(18) cm(-3), was produced in an electromagnetic shock tube. The density gradient created by the reflected plasma was large enough to produce measurable refraction of the laser beam. The laser cavity, which was initially misaligned, attained perfect alignment when the plasma was introduced into the cavity.

On possible structures of normal ionizing shock waves in electromagnetic shock tubes

The problem of possible structures of normal ionizing shock waves is studied. On the basis of the general theory of ionizing shock waves in magnetic fields previously developed Liberman and Velikovich, 1981, a similarity solution of the piston problem for an impenetrable piston and a magnetic piston is described and a numerical solution of the non-stationary piston problem is obtained. It is shown that precursor photo-ionization of the neutral gas by the radiation of the shock-heated gas is the dominant factor in shaping normal ionizing shock structures. In particular, it is shown that the strong overheating of atoms and ions in shock fronts is due to the tensor form of Ohm's law in the precursor region. The conditions of formation of type 3 and type 4 shock structures are elucidated together with the limits of applicability of the Chapman-Jouguet hypothesis. The theory is applied to the interpretation of the experimental data on normal ionizing shock waves.

Mode-locking observation of a CO2 laser by intracavity plasma injection

A TEA CO2 laser was simultaneously Q-switched and mode-locked when an underdense plasma was injected into the cavity. The plasma was produced in an electromagnetic shock tube. Plasma density and temperature were Ne ~ 1017 cm−3 and Te ~ 2 eV, respectively. Phase perturbation of the cavity due to the time dependent plasma refractive index could account for the observed mode-locking.