Showing papers on "Relativistic plasma published in 2005"

Scalings for ultrarelativistic laser plasmas and quasimonoenergetic electrons

Abstract: The similarity theory is derived for ultrarelativistic laser-plasma interactions. It is shown that the most fundamental S similarity is valid for both underdense and overdense plasmas. The particular case of tenious plasma is considered in great detail. It is shown that the electron dynamics in this case has two characteristic scales. The fast scale corresponds to relaxation to some attractor solution. The slow dynamics describes an adiabatic evolution of this attractor. This leads to a remarkable wave breaking exclusion rule in the three-dimensional geometry. A similarity theory for the slow dynamics allows obtaining simple “engineering” scalings for the maximum electron energies, the number of accelerated electrons, the electron beam density, and for the acceleration distance. These scalings are aimed at design of a compact high-energy laser-plasma accelerator generating electron beams suitable for practical applications.

Simulations of relativistic collisionless shocks: shock structure and particle acceleration

Abstract: We discuss 3D simulations of relativistic collisionless shocks in electron-positron pair plasmas using the particle-in-cell (PIC) method. The shock structure is mainly controlled by the shock's magnetization (''sigma'' parameter). We demonstrate how the structure of the shock varies as a function of sigma for perpendicular shocks. At low magnetizations the shock is mediated mainly by the Weibel instability which generates transient magnetic fields that can exceed the initial field. At larger magnetizations the shock is dominated by magnetic reflections. We demonstrate where the transition occurs and argue that it is impossible to have very low magnetization collisionless shocks in nature (in more than one spatial dimension). We further discuss the acceleration properties of these shocks, and show that higher magnetization perpendicular shocks do not efficiently accelerate nonthermal particles in 3D. Among other astrophysical applications, this may pose a restriction on the structure and composition of gamma-ray bursts and pulsar wind outflows.

Multi-GeV energy gain in a plasma-wakefield accelerator.

Abstract: A plasma-wakefield accelerator has accelerated particles by over 2.7 GeV in a 10 cm long plasma module. A 28.5 GeV electron beam with 1.8 x 10(10) electrons is compressed to 20 microm longitudinally and focused to a transverse spot size of 10 microm at the entrance of a 10 cm long column of lithium vapor with density 2.8 x 10(17) atoms/cm3. The electron bunch fully ionizes the lithium vapor to create a plasma and then expels the plasma electrons. These electrons return one-half plasma period later driving a large amplitude plasma wake that in turn accelerates particles in the back of the bunch by more than 2.7 GeV.

Nonlinear Zakharov–Kuznetsov equation for obliquely propagating two-dimensional ion-acoustic solitary waves in a relativistic, rotating magnetized electron-positron-ion plasma

Abstract: The purpose of this work is to investigate the linear and nonlinear properties of the ion-acoustic waves (IAW), propagating obliquely to an external magnetic field in a weakly relativistic, rotating, and magnetized electron-positron-ion plasma. The Zakharov–Kuznetsov equation is derived by employing the reductive perturbation technique for this wave in the nonlinear regime. This equation admits the solitary wave solution. The amplitude and width of this solitary wave have been discussed with the effects of obliqueness, relativity, ion temperature, positron concentration, magnetic field, and rotation of the plasma and it is observed that for IAW these parameters affect the propagation properties of solitary waves and these plasmas behave differently from the simple electron-ion plasmas. Likewise, the current density and electric field of these waves are investigated for their dependence on the above-mentioned parameters.

Observation of Laser-Pulse Shortening in Nonlinear Plasma Waves

Abstract: We have measured the temporal shortening of an ultraintense laser pulse interacting with an underdense plasma. When interacting with strongly nonlinear plasma waves, the laser pulse is shortened from $38\ifmmode\pm\else\textpm\fi{}2\text{ }\text{ }\mathrm{fs}$ to the 10--14 fs level, with a 20% energy efficiency. The laser ponderomotive force excites a wakefield, which, along with relativistic self-phase modulation, broadens the laser spectrum and subsequently compresses the pulse. This mechanism is confirmed by 3D particle in cell simulations.

The influence of an ambient magnetic field on relativistic collisionless plasma shocks

Abstract: Plasma outflows from gamma-ray bursts, supernovae, and relativistic jets, in general, interact with the surrounding medium through collisionless shocks. The microphysics of such shocks are still poorly understood, which, potentially, can introduce uncertainties in the interpretation of observations. It is now well established that the Weibel two-stream instability is capable of generating strong electromagnetic fields in the transition region between the jet and the ambient plasma. However, the parameter space of collisionless shocks is vast and still remains unexplored. In this Letter, we focus on how an ambient magnetic field affects the evolution of the electron Weibel instability and the associated shock. Using a particle-in-cell code, we have performed three-dimensional numerical experiments on such shocks. We compare simulations in which a jet is injected into an unmagnetized plasma with simulations in which the jet is injected into a plasma with an ambient magnetic field both parallel and perpendicular to the jet flow. We find that there exists a threshold of the magnetic field strength below which the Weibel two-stream instability dominates, and we note that the interstellar medium magnetic field strength lies well below this value. In the case of a strong magnetic field parallel to the jet, the Weibel instability is quenched. In the strong perpendicular case, ambient and jet electrons are strongly accelerated because of the charge separation between deflected jet electrons and less deflected jet ions. Also, the electromagnetic topologies become highly nonlinear and complex with the appearance of antiparallel field configurations.

Time-dependent Numerical Model for the Emission of Radiation from Relativistic Plasma

Abstract: We describe a numerical model constructed for the study of the emission of radiation from relativistic plasma under conditions characteristic of, e.g., gamma-ray bursts and active galactic nuclei. The model solves self-consistently the kinetic equations for e± and photons, describing cyclosynchrotron emission, direct Compton and inverse Compton scattering, and pair production and annihilation, including the evolution of high-energy electromagnetic cascades. The code allows calculations over a wide range of particle energies, spanning more than 15 orders of magnitude in energy and timescales. Our unique algorithm, which enables to follow the particle distributions over a wide energy range, allows us to accurately derive spectra at high energies, >100 TeV. We present the kinetic equations that are being solved, a detailed description of the equations describing the various physical processes, the solution method, and several examples of numerical results. Excellent agreement with analytical results of the synchrotron-synchrotron self-Compton model is found for parameter-space regions in which this approximation is valid, and several examples are presented of calculations for parameter-space regions for which analytic results are not available.

Electron acceleration by lower hybrid waves in magnetic reconnection regions

Abstract: A new model for electron acceleration in magnetic reconnection regions is developed analytically, tested using quasilinear simulations, and the qualitative predictions compared with observations of reconnection in Earth’s magnetotail and the solar corona. The model involves lower hybrid (LH) waves, produced by a drift instability (LHDI) in reconnection regions, stochastically accelerating electrons parallel to the magnetic field by the Cherenkov resonance (LH drive or LHD). Analytic theory shows that LH waves produced by LHDI have the correct wave numbers to cause parallel electron acceleration from thermal to highly superthermal and even relativistic energies, for sufficiently low plasma β and long evolution times. Several previous Vlasov and particle-in-cell simulations show growth of LH waves by LHDI. Assuming that LHDI produces LH waves with the wave numbers and energy densities (≈50% that of the thermal ion plasma) found in the Vlasov simulations, quasilinear simulations with the correct mass ratio s...

Three-dimensional evolution of a relativistic current sheet: triggering of magnetic reconnection by the guide field.

Abstract: The linear and nonlinear evolution of a relativistic current sheet of pair (${e}^{\ifmmode\pm\else\textpm\fi{}}$) plasmas is investigated by three-dimensional particle-in-cell simulations. In a Harris configuration, it is obtained that the magnetic energy is fast dissipated by the relativistic drift kink instability (RDKI). However, when a current-aligned magnetic field (the so-called ``guide field'') is introduced, the RDKI is stabilized by the magnetic tension force and it separates into two obliquely propagating modes, which we call the relativistic drift-kink-tearing instability. These two waves deform the current sheet so that they trigger relativistic magnetic reconnection at a crossover thinning point. Since relativistic reconnection produces a lot of nonthermal particles, the guide field is of critical importance to study the energetics of a relativistic current sheet.

Envelope solitons associated with electromagnetic waves in a magnetized pair plasma

Abstract: The amplitude modulation of magnetic field-aligned circularly polarized electromagnetic (CPEM) waves in a magnetized pair plasma is reexamined. The nonlinear frequency shifts include the effects of the radiation pressure driven density and compressional magnetic field perturbations as well as relativistic particle mass variations. The dynamics of the modulated CPEM wave packets is governed by a nonlinear Schrodinger equation, which has attractive and repulsive interaction potentials for fast and slow CPEM waves. The modulational stability of a constant amplitude CPEM wave is studied by deriving a nonlinear dispersion from the cubic Schrodinger equation. The fast (slow) CPEM mode is modulationally unstable (stable). Possible stationary amplitude solutions of the modulated fast (slow) CPEM mode can be represented in the form of bright and dark/gray envelope electromagnetic soliton structures. Localized envelope excitations can be associated with the microstructures in pulsar magnetospheres and in laboratory...

Laser wakefield acceleration by petawatt ultrashort laser pulses

Abstract: An ultrashort (about 30fs) petawatt laser pulse focused with a wide focal spot (about 100μm) in a rarefied plasma (n0∼1017cm−3) excites a nonlinear plasma wakefield which can accelerate injected electrons up to GeV energies without any pulse channeling. Under these conditions, propagation of the laser pulse with an overcritical power for relativistic self-focusing is almost the same as in vacuum. The nonlinear quasiplane plasma wave, whose amplitude and phase velocity vary along the laser path, effectively traps and accelerates injected electrons with a wide range of initial energies. Electrons accelerated over two Rayleigh lengths (about 8cm) can gain energies up to 1Gev. In particular, the electrons trapped from a long (τb∼330fs) nonresonant electron beamlet of 1MeV particles eventually form a low emittance bunch with energies in the range 900±50MeV. These conclusions follow from two-dimensional simulations performed in cylindrical geometry by means of the fully relativistic time-averaged particle code ...

Quasi-monoenergetic electron beam generation during laser pulse interaction with very low density plasmas

Abstract: The results of experiments are presented for the single laser pulse interaction with a very low density gas target, under the conditions when the generated wake wave is below the wave-breaking threshold and the laser pulse power is lower than the critical power for relativistic self-focusing. A quasi-monoenergetic electron beam is found to be stably generated for various laser pulse intensity values by controlling the acceleration length. The results of two-dimensional particle-in-cell simulations show that for the electron acceleration an additional mechanism of electron injection into the acceleration phase is required. It is demonstrated that the longitudinal inhomogeneity of the plasma density leads to the electron injection.

Shock formation at the magnetic collimation of relativistic jets

Abstract: If the observed relativistic plasma outflows in astrophysical jets are magnetically collimated and a single-component model is adopted, consisting of a wind-type outflow from a central object, then a problem arises with the inefficiency of magnetic self-collimation to collimate a sizeable portion of the mass and magnetic fluxes in the relativistic outflow from the central object. To solve this dilemma, we have applied the mechanism of magnetic collimation to a two-component model consisting of a relativistic wind-type outflow from a central source and a non-relativistic wind from a surrounding disc. By employing a numerical code for a direct numerical solution of the steady-state problem in the zone of super-fast magnetized flow, which allows us to perform a determination of the flow with shocks, it is shown that in this two-component model it is possible to collimate into cylindrical jets all the mass and magnetic fluxes that are available from the central source. In addition, it is shown that the collimation of the plasma in this system is usually accompanied by the formation of oblique shock fronts. The non-relativistic disc-wind not only plays the role of the jet collimator, but it also induces the formation of shocks as it collides with the initially radial inner relativistic wind and also as the outflow is reflected by the system axis. Another interesting feature of this process of magnetic collimation is a sequence of damped oscillations in the width of the jet.

Relativistic attosecond physics

Abstract: A study, with particle-in-cell simulations, of relativistic nonlinear optics in the regime of tight focus and ultrashort pulse duration (the λ3 regime) reveals that synchronized attosecond electromagnetic pulses [N. M. Naumova, J. A. Nees, I. V. Sokolov, B. Hou, and G. A. Mourou, Phys. Rev. Lett. 92, 063902 (2004)] and attosecond electron bunches [N. Naumova, I. Sokolov, J. Nees, A. Maksimchuk, V. Yanovsky, and G. Mourou, Phys. Rev. Lett. 93, 195003 (2004)] emerge efficiently from laser interaction with overdense plasmas. The λ3 concept enables a more basic understanding and a more practical implementation of these phenomena because it provides spatial and temporal isolation. The synchronous generation of strong attosecond electromagnetic pulses and dense attosecond electron bunches provides a basis for relativistic attosecond optoelectronics.

Hierarchy of beam plasma instabilities up to high beam densities for fast ignition scenario

Abstract: The hierarchy of electromagnetic instabilities suffered by a relativistic electron beam passing through a plasma is investigated. The fluid approximation is used and beam densities up to the plasma one are considered. The hierarchy between instabilities is established in terms of two parameters only: the beam relativistic factor and the ratio nb∕np of the beam density to the plasma one. It is found that for nb∕np≲0.53, the most unstable modes are a mix between filamentation and two-stream instabilities. Beyond this limit, filamentation instability may dominate, depending on the beam relativistic factor. The largest growth rates are found for a beam density slightly smaller than the plasma one.

Dynamics of a Xe cluster plasma produced by an intense ultrashort pulse KrF laser

Abstract: The dynamics of Xe clusters with initial radius between 10 and 100 A irradiated by an IR subpicosecond laser pulse is investigated The evolution of the cluster is modeled with a relativistic time-dependent three-dimensional particle simulation model The focus of this investigation is to understand the energy absorption of clusters and how the absorbed energy is distributed among the various degrees of freedom The consequence of the initial cluster radius on the absorbed energy, average charge per atom, mean electron and ion energies, ionization, removal of electrons from the cluster, and cluster expansion was studied The absorbed energy per cluster scales as N5∕3, and the mean electron and ion energies scale as N1∕3 and N2∕3, respectively (N is the number of atoms per cluster) A significant fraction of the absorbed energy (∼90%) is converted into kinetic energy with comparable contribution to electrons and ions The energy balance suggests that smaller clusters are more efficient as radiators, while

Parametric mechanism of the rotation energy pumping by a relativistic plasma

Abstract: An investigation of the kinematics of a plasma stream rotating in the pulsar magnetosphere is presented. On the basis of an exact set of equations describing the behavior of the plasma stream, the increment of the instability is obtained, and the possible relevance of this approach for the understanding of the pulsar rotation energy pumping mechanism is discussed.

Heating the bubbly gas of galaxy clusters with weak shocks and sound waves

Abstract: Using hydrodynamic simulations and a technique to extract the rotational component of the velocity field, we show how bubbles of relativistic gas inflated by AGN jets in galaxy clusters act as a catalyst, transforming the energy carried by sound and shock waves into heat. The energy is stored in a vortex field around the bubbles, which can subsequently be dissipated. The efficiency of this process is set mainly by the fraction of the cluster volume filled by (sub-) kiloparsec-scale filaments and bubbles of relativistic plasma.

Plasma channel charging by an intense short pulse laser and ion Coulomb explosion

Abstract: The combined effects of relativistic self-focusing and the expulsion of electrons by the ponderomotive force of a radially focused laser create an ion channel, depleted of electrons, of radius r0∼c∕ωp, where ωp is the electron plasma frequency. This charging process takes place on plasma period, ωp−1, time scale. The Coulomb explosion of the channel accelerates ions to several hundreds of keV energy in about an ion plasma period, constituting an important ion acceleration mechanism by short pulse intense laser. In the case of a deuterium-tritium plasma, the accelerated ions can produce fusion energy with an efficiency of ∼0.5%.

Gamma-Ray Bursts, Collisionless Shocks and Synthetic Spectra

Abstract: The radiation from afterglows of gamma-ray bursts (GRB) is generated in collisionless plasma shocks. The two main ingredients behind the radiation are high-energy, non-thermal electrons and a strong magnetic field. I argue that in order to make the right conclusions about gamma-ray burst and afterglow parameters from observations, it is crucial to have a firm understanding of the microphysics of collisionless shock. I present the results of self-consistent, three-dimensional particle-in-cell computational simulations of the collision of weakly magnetized plasma shells: The experiments show how a plasma instability generates a magnetic field in the shock. The field has strength up to percents of the equipartition value. The experiments also reveal a new, non-thermal electron acceleration mechanism that differs substantially from Fermi acceleration. Finally, I present the results from a new numerical tool that enables us to extract synthetic radiation spectra directly from the experiments. The preliminary results differ from synchrotron radiation but are consistent with GRB afterglow observations. I conclude that strong magnetic field generation, non-thermal particle acceleration and the emission of radiation that is consistent with GRB afterglow observations, are all unavoidable consequences of the collision between two relativistic plasma shells.

On The Method Of Estimating Emission Altitude from Relativistic Phase Shift in Pulsars

Abstract: The radiation by relativistic plasma particles is beamed in the direction of field-line tangents in the corotating frame, but in an inertial frame it is aberrated toward the direction of rotation. We have revised the relation of aberration phase shift by taking into account the magnetic colatitude and azimuth of the emission spot and the plasma rotation velocity. In the limit of the small-angle approximation, the aberration phase shift becomes independent of the inclination angle α and the sight line impact angle β. However, at larger altitudes or larger rotation phases, the shift does depend on α and β. We have given an expression for the phase shift in the intensity profile by taking into account aberration, retardation, and polar cap currents.

Modeling of clusters in a strong 248-nm laser field by a three-dimensional relativistic molecular dynamic model.

Abstract: A relativistic time-dependent three-dimensional particle simulation model has been developed to study the interaction of intense ultrashort KrF (248 nm) laser pulses with small Xe clusters. The trajectories of the electrons and ions are treated classically according to the relativistic equation of motion. The model has been applied to a different regime of ultrahigh intensities extending to 10{sup 21} W/cm{sup 2}. In particular, the behavior of the interaction with the clusters from intensities of {approx}10{sup 15} W/cm{sup 2} to intensities sufficient for a transition to the so-called 'collective oscillation model' has been explored. At peak intensities below 10{sup 20} W/cm{sup 2}, all electrons are removed from the cluster and form a plasma. It is found that the 'collective oscillation model' commences at intensities in excess of 10{sup 20} W/cm{sup 2}, the range that can be reached in stable relativistic channels. At these high intensities, the magnetic field has a profound effect on the shape and trajectory of the electron cloud. Specifically, the electrons are accelerated to relativistic velocities with energies exceeding 1 MeV in the direction of laser propagation and the magnetic field distorts the shape of the electron cloud to give the form of a pancake.

Cross focusing of two laser beams and plasma wave excitation

Abstract: This article presents the cross focusing of two high power laser beams in a plasma when relativistic and ponderomotive nonlinearities are operative. The effect of electron density modification changes the critical power significantly in contrast to (only) relativistic case. The plasma wave generation at the difference frequency and particle acceleration has also been studied. In a typical case when laser wavelengths are 1047 and 1064nm and electron density 1.9×1019cm−3, the maximum electron plasma wave power flux comes out to be 6×1017W∕cm2 (laser power P1=3.6×1018W∕cm2 and P2=3.2×1018W∕cm2).

Modulation instability of laser pulse in magnetized plasma

Abstract: Modulation instability of a laser pulse propagating through transversely magnetized underdense plasma is studied. It is observed that interaction of laser radiation with plasma in the presence of uniform magnetic field results in an additional perturbed transverse plasma current density along with the relativistic and ponderomotive nonlinear current densities, thus affecting the modulational interaction. In the plane wave limit it is observed that modulational interaction is more stable for magnetized plasma as compared to the unmagnetized case. The analysis shows that there is a significant reduction in the growth rate of modulation instability over a given range of unstable wave numbers due to magnetization of plasma.

Dynamics of intense laser channel formation in an underdense plasma

Abstract: Efficient guiding and propagation of multi-keV x-rays in plasmas can be achieved by dynamically modifying the media through plasma channel formation. The dynamics of plasma channel formation is studied in preformed underdense plasma irradiated by a high intensity laser. This is done by a two-dimensional model coupling laser propagation to a relativistic particle-in-cell model. For laser intensity of 1020W∕cm2 and a laser beam width of 5μm the channel formation proceeds on a time scale of 60–70fs in uniform plasma with density 1018cm−3. The channel closes shortly after the rear of the laser pulse has passed due to Coulomb attraction from the ion core. Electron cavitation occurs only if the laser intensity is above a certain threshold intensity and the laser pulse duration exceeds 100fs. X-ray generation and propagation is feasible for ultrarelativistic laser pulses with small beam width, less than ∼20μm, and duration of more than 100fs.

Localization of intense electromagnetic waves in a relativistically hot plasma

Abstract: We consider nonlinear interactions between intense short electromagnetic waves (EMWs) and a relativistically hot electron plasma that supports relativistic electron holes (REHs). It is shown that such EMW-REH interactions are governed by a coupled nonlinear system of equations composed of a nonlinear Schrodinger equation describing the dynamics of the EMWs and the Poisson-relativistic Vlasov system describing the dynamics of driven REHs. The present nonlinear system of equations admits both a linearly trapped discrete number of eigenmodes of the EMWs in a quasistationary REH and a modification of the REH by large-amplitude trapped EMWs. Computer simulations of the relativistic Vlasov and Maxwell-Poisson system of equations show complex interactions between REHs loaded with localized EMWs.

Covariant kinetic dispersion theory of linear waves in anisotropic plasmas. III. Counterstreaming plasmas

Abstract: The properties of longitudinal and transverse oscillations in unmagnetized counterstreaming Maxwellian plasmas of arbitrary composition for waves propagating parallel to the stream direction are investigated on the basis of Maxwell equations and the relativistic Vlasov equation. These dispersion relations describe the linear response of the system to the initial perturbations and thus define all existing linear parallel propagating plasma modes in the system. By analytic continuation the dispersion relations in the whole complex frequency plane are constructed. The dispersion relations hold for any values of the plasma temperatures, streaming velocity, intensities of the two streams, and for all wave number and frequency values of the oscillations. In the limit of nonrelativistic plasma temperatures these general dispersion relations can be expressed in terms of the well-documented Fried and Conte plasma dispersion function. Only in the case of infinitely large speed of light they agree with the standard nonrelativistic results.

Electron inertia contribution to soliton evolution in an inhomogeneous weakly relativistic two-fluid plasma

Abstract: The contribution of electron inertia to the evolution of solitons in weakly and strongly inhomogeneous plasmas having streaming ions and electrons with weak relativistic effect is studied on the basis of a relevant Korteweg–de Vries equation derived with the help of reductive perturbation technique. Three types of modes (fast, medium, and slow) are found to propagate in the plasma. In case of weak (strong) inhomogeneous plasma, only the fast (slow) mode corresponds to the soliton evolution. For the propagation of solitons in strongly inhomogeneous plasma, there is no restriction on the ion and electron velocities but in case of weak inhomogeneity the solitons are possible only for a particular range of velocity difference. This range shows the dependence on the temperature and mass ratios of the ions and electrons. In addition, it is realized that only the rarefactive solitons are possible in the present plasma model. The effect of electron inertia on the phase velocity, peak soliton amplitude, and solito...

Coherent radiation of relativistic nonlinear Thomson scattering

Abstract: The condition for the coherent addition of the relativistic nonlinear Thomson scattered (RNTS) radiations from a group of electrons is derived. Numerical calculations show that under such a condition, all the characteristics of RNTS radiation by a single electron are maintained, leading to the generation of intense attosecond x rays. Such an attosecond x ray is produced in a specific direction with a very narrow angular divergence. An x-ray radiation of ∼1016W∕cm2 with a pulse width of 7.7 as is expected for an oblique irradiation of a 20 fs linearly polarized laser pulse of 4×1019W∕cm2 on a 7 nm thick film target. For the proof-of-principle experiment, the radiation characteristics from a 50 nm thick film target are presented and discussed.

Study of the mechanism for fast ion heating in the GOL-3 multimirror magnetic confinement system

Abstract: Results are presented from experimental studies of ion heating in the GOL-3 device. The experiments were carried out in a multimirror configuration with a local magnetic well. It was found that, during the injection of a relativistic electron beam, a decrease in the local density of the beam in a magnetic well, which is proportional to the decrease in the strength of the longitudinal magnetic field, results in the formation of a short plasma region with a low electron temperature. The measured longitudinal gradient of the plasma pressure corresponds to an electron temperature gradient of ∼2–3 keV/m. Axially nonuniform heating of the plasma electrons gives rise to the macroscopic motion of the plasma along the magnetic field in each cell of the multimirror confinement system. The mixing of the counterpropagating plasma flows inside each cell leads to fast ion heating. Under the given experimental conditions, the efficiency of this heating mechanism is higher than that due to binary electron-ion collisions. The collision and mixing of the counterpropagating plasma flows is accompanied by a neutron and γ-ray burst. The measured ratio of the plasma pressure to the vacuum magnetic field pressure in these experiments reaches 0.2.