Thermonuclear Detonation Wave Research Articles

Confronting double-detonation sub-Chandrasekhar models with the low-luminosity suppression of Type Ia supernovae

ABSTRACT Type Ia supernovae (SNe Ia) are likely the thermonuclear explosions of carbon–oxygen (CO) white-dwarf (WD) stars, but their progenitor systems remain elusive. Recently, Sharon & Kushnir used The Zwicky Transient Facility Bright Transient Survey to construct a synthesized 56Ni mass, MNi56, distribution of SNe Ia. They found that the rate of low-luminosity ($M_\text{Ni56}\approx 0.15\, \mathrm{M}_{\odot }$) SNe Ia is lower by a factor of ∼10 than the more common $M_\text{Ni56}\approx 0.7\, \mathrm{M}_{\odot }$ events. We here show that in order for the double-detonation model (DDM, in which a propagating thermonuclear detonation wave, TNDW, within a thin helium shell surrounding a sub-Chandrasekhar mass CO core triggers a TNDW within the core) to explain this low-luminosity suppression, the probability of a low-mass ($\approx 0.85\, \mathrm{M}_{\odot }$) WD explosion should be ∼100-fold lower than that of a high-mass ($\approx 1.05\, \mathrm{M}_{\odot }$) WD. One possible explanation is that the ignition of low-mass CO cores is somehow suppressed. We use accurate one-dimensional numerical simulations to show that if a TNDW is able to propagate within the helium shell, then the ignition within the CO core is guaranteed (resolved here for the first time in a full-star simulation), even for $0.7\, \mathrm{M}_{\odot }$ WDs, providing no natural explanation for the low-luminosity suppression. DDM could explain the low-luminosity suppression if the mass distribution of primary WDs in close binaries is dramatically different from the field distribution; if the Helium shell ignition probability is suppressed for low-mass WDs; or if multidimensional perturbations significantly change our results.

An accurate and efficient numerical calculation of detonation waves in multidimensional supernova simulations using a burning limiter and adaptive quasi-statistical equilibrium

ABSTRACT Resolving the small length-scale of thermonuclear detonation waves (TNDWs) in supernovae is currently not possible in multidimensional full-star simulations. Additionally, multidimensional simulations usually use small, oversimplistic reaction networks and adopt an ad hoc transition criterion to nuclear statistical equilibrium (NSE). The errors due to the applied approximations are not well understood. We present here a new accurate and efficient numerical scheme that accelerates the calculations by orders of magnitudes and allows the structure of TNDWs to be resolved. The numerical scheme has two important ingredients: (1) a burning limiter that broadens the width of the TNDW while accurately preserving its internal structure, and (2) an adaptive separation of isotopes into groups that are in nuclear statistical quasi-equilibrium, which resolves the time-consuming burning calculation of reactions that are nearly balanced out. Burning is calculated in situ employing the required large networks without the use of post-processing or pre-describing the conditions behind the TNDW. In particular, the approach to and deviation from NSE are calculated self-consistently. The scheme can be easily implemented in multidimensional codes. We test our scheme against accurate solutions of the structure of TNDWs and against homogeneous expansion from NSE. We show that with resolutions that are typical for multidimensional full-star simulations, we reproduce the accurate thermodynamic trajectory (density, temperature, etc.) to an accuracy that is better than a per cent for the resolved scales (where the burning limiter is not applied), while keeping the error for unresolved scales (broadened by the burning limiter) within a few per cent.

The structure of detonation waves in supernovae revisited

The structure of a thermonuclear detonation wave can be solved accurately and, thus, may serve as a test bed for studying different approximations that are included in multidimensional hydrodynamical simulations of supernova. We present the structure of thermonuclear detonations for the equal mass fraction of $^{12}$C and $^{16}$O (CO) and for pure $^{4}$He (He) over a wide range of upstream plasma conditions. The lists of isotopes we constructed allow us to determine the detonation speeds, as well as the final states for these detonations, with an uncertainty of the percent level (obtained here for the first time). We provide our results with a numerical accuracy of $\sim0.1\%$, which provides an efficient benchmark for future studies. We further show that CO detonations are pathological for all upstream density values, which differs from previous studies, which concluded that for low upstream densities CO detonations are of the Chapman-Jouget (CJ) type. We provide an approximate condition, independent of reaction rates, that allows to estimate whether arbitrary upstream values will support a detonation wave of the CJ type. Using this argument, we are able to show that CO detonations are pathological and to verify that He detonations are of the CJ type, as was previously claimed for He. Our analysis of the reactions that control the approach to nuclear statistical equilibrium, which determines the length-scale of this stage, reveals that at high densities, the reactions $^{11}$B$+p\leftrightarrow3^{4}$He plays a significant role, which was previously unknown.

FAILURE OF A NEUTRINO-DRIVEN EXPLOSION AFTER CORE-COLLAPSE MAY LEAD TO A THERMONUCLEAR SUPERNOVA

We demonstrate that $\sim10\,\textrm{s}$ after the core-collapse of a massive star, a thermonuclear explosion of the outer shells is possible for some (tuned) initial density and composition profiles, assuming that the neutrinos failed to explode the star. The explosion may lead to a successful supernova, as first suggested by Burbidge et al. We perform a series of one-dimensional (1D) calculations of collapsing massive stars with simplified initial density profiles (similar to the results of stellar evolution calculations) and various compositions (not similar to 1D stellar evolution calculations). We assume that the neutrinos escaped with a negligible effect on the outer layers, which inevitably collapse. As the shells collapse, they compress and heat up adiabatically, enhancing the rate of thermonuclear burning. In some cases, where significant shells of mixed helium and oxygen are present with pre-collapsed burning times of $\lesssim100\,\textrm{s}$ ($\approx10$ times the free-fall time), a thermonuclear detonation wave is ignited, which unbinds the outer layers of the star, leading to a supernova. The energy released is small, $\lesssim10^{50}\,\textrm{erg}$, and negligible amounts of synthesized material (including $^{56}$Ni) are ejected, implying that these 1D simulations are unlikely to represent typical core-collapse supernovae. However, they do serve as a proof of concept that the core-collapse-induced thermonuclear explosions are possible, and more realistic two-dimensional and three-dimensional simulations are within current computational capabilities.

Collision of plane thermonuclear detonation waves in a preliminarily compressed DT mixture

The paper deals with a one-dimensional problem on symmetric irradiation of a plane DT fuel layer with a thickness 2H and density ρ0 ⩽ 100ρs (where ρs is the density of the DT fuel in the solid state at atmospheric pressure and a temperature of 4 K) by two identical monoenergetic proton beams with a kinetic energy of 1 MeV, an intensity of 1019 W/cm2, and a duration of 50 ps. The problem is solved in the framework of one-fluid two-temperature hydrodynamic model that takes into account the equation of state for hydrogen, electron and ion heat conductivities, kinetics of the DT reaction, plasma self-radiation, and plasma heating by α-particles. The irradiation of the fuel results in the appearance of two counterpropagating detonation waves to the fronts of which rarefaction waves are adjacent. The efficiency of the DT reaction after the collision (reflection from the plane of symmetry) of the detonation waves depends on the spatial homogeneity of thermodynamic functions between the fronts of the reflected detonation waves. At Hρ0 ≈ 1 g/cm2, the gain factor is G ≈ 200, whereas at Hρ0 ≈ 5 g/cm2, it is G > 2000. As applied to a cylindrical target that is ignited from ends and in which the cylinder with the fuel is surrounded by a heavy magnetized shell, the obtained values of the burn-up and gain factors are maximum possible. To estimate the ignition energy Eig of a cylindrical target by using solutions to the one-dimensional problem, a quasi-one-dimensional model is developed. The model assumes that the main mechanism of target ignition is fuel heating by α-particles. The trajectories of α-particles are limited by a cylindrical surface with a given radius, which is a parameter of the model and is identified with the fuel radius in the target and the radii of the irradiating proton beams. This model reproduces the well-known theoretical dependence Eig ∼ ρ0−2 and yields Eig = 160 kJ as a lower estimate of the ignition energy for ρ0 = 100ρs ≈ 22 g/cm3.

Plane thermonuclear detonation waves initiated by proton beams and quasi-one-dimensional model of fast ignition

AbstractThe one-dimensional problem on bilatiral irradiation by proton beams of the plane layer of condensed DT mixture with length 2H and density ρ0 ≤ 100ρs, where ρs is the fuel solid-state density at atmospheric pressure and temperature of 4 K, is considered. The proton kinetic energy is 1 MeV, the beam intensity is 1019 W/cm2 and duration is 50 ps. A mathematical model is based on the one-fluid two-temperature hydrodynamics with a wide-range equation of state of the fuel, electron and ion heat conduction, DT fusion reaction kinetics, self-radiation of plasma and plasma heating by α-particles. If the ignition occurs, a plane detonation wave, which is adjacent to the front of the rarefaction wave, appears. Upon reflection of this detonation wave from the symmetry plane, the flow with the linear velocity profile along the spatial variable x and with a weak dependence of the thermodynamic functions of x occurs. An appropriate solution of the equations of hydrodynamics is found analytically up to an arbitrary constant, which can be chosen so that the analytical solution describes with good accuracy the numerical one. The gain with respect to the energy of neutrons G ≈ 200 at Hρ0 ≈ 1 g/cm2, and G > 2000 at Hρ0 ≈ 5 g/cm2. To evaluate the ignition energy Eig of cylindrical targets, the quasi-1D model, limiting trajectories of α-particles by a cylinder of a given radius, is suggested. The model reproduces the known theoretical dependence Eig ~ ρ0−2 and gives Eig = 160 kJ for ρ0 = 100ρs ≈ 22 g/cm3.

Ultra-dense deuterium and cold fusion claims

An attempt is made to explain the recently reported occurrence of 14 MeV neutron induced nuclear reactions in deuterium metal hydrides as the manifestation of a slightly radioactive ultra-dense form of deuterium, with a density of 130,000 g/cm 3 observed by a Swedish research group through the collapse of deuterium Rydberg matter. In accordance with this observation it is proposed that a large number of deuterons form a “linear-atom” supermolecule. By the Madelung transformation of the Schrödinger equation, the linear deuterium supermolecule can be described by a quantized line vortex. A vortex lattice made up of many such supermolecules is possible only with deuterium, because deuterons are bosons, and the same is true for the electrons, which by the electron–phonon interaction in a vortex lattice form Cooper pairs. It is conjectured that the latent heat released by the collapse into the ultra-dense state has been misinterpreted as cold fusion. Hot fusion though, is here possible through the fast ignition of a thermonuclear detonation wave from a hot spot made with a 1 kJ 10 petawatt laser in a thin slice of the ultra-dense deuterium.

Deuterium microbomb rocket propulsion

Large scale manned space flight within the solar system is still confronted with the solution of two problems: (1) A propulsion system to transport large payloads with short transit times between different planetary orbits. (2) A cost effective lifting of large payloads into earth orbit. For the solution of the first problem a deuterium fusion bomb propulsion system is proposed where a thermonuclear detonation wave is ignited in a small cylindrical assembly of deuterium with a gigavolt-multimegaampere proton beam, drawn from the magnetically insulated spacecraft acting in the ultrahigh vacuum of space as a gigavolt capacitor. For the solution of the second problem, the ignition is done by argon ion lasers driven by high explosives, with the lasers destroyed in the fusion explosion and becoming part of the exhaust.

Fast ignition by detonation in a hydrodynamic flow

A general concept of fast ignition by a hydrodynamic pulse is developed. The main statements of the concept are formulated having in mind the need to ignite the pre-compressed thermonuclear fuel of the inertial confinement fusion (ICF) target. Initially, combustion must be initiated inside the hydrodynamic flow during its action on the target. The conditions for propagating a self-sustaining thermonuclear-detonation wave from an igniter on the thermonuclear fuel of the ICF-target must be provided. For this, the deuterium–tritium (DT) igniter placed in the forward part of the hydrodynamic flow should not only be heated up to thermonuclear temperature, but also compressed to a density close to the density of the ICF-target fuel. It is shown that the detonation of the multilayer conical target (containing DT-ice and a heavy pusher) enables fast ignition of the ICF target fuel of 200–500 g/cm3 density at an implosion velocity of 300–500 km/s.

Ignition of a Deuterium Micro-Detonation with a Gigavolt Super Marx Generator

The Centurion–Halite experiment demonstrated the feasibility of igniting a deuterium–tritium micro-explosion with an energy of not more than a few megajoule, and the Mike test, the feasibility of a pure deuterium explosion with an energy of more than 106 MJ. In both cases the ignition energy was supplied by a fission bomb explosive. While an energy of a few megajoule, to be released in the time required of less than 10−9 s, can be supplied by lasers and intense particle beams, this is not enough to ignite a pure deuterium explosion. Because the deuterium–tritium reaction depends on the availability of lithium, the non-fission ignition of a pure deuterium fusion reaction would be highly desirable. It is shown that this goal can conceivably be reached with a “Super Marx Generator”, where a large number of “ordinary” Marx generators charge (magnetically insulated) fast high voltage capacitors of a second stage Marx generator, called a “Super Marx Generator”, ultimately reaching gigavolt potentials with an energy output in excess of 100 MJ. An intense 107 Ampere-GeV proton beam drawn from a “Super Marx Generator” can ignite a deuterium thermonuclear detonation wave in a compressed deuterium cylinder, where the strong magnetic field of the proton beam entraps the charged fusion reaction products inside the cylinder. In solving the stand-off problem, the stiffness of a GeV proton beam permits to place the deuterium target at a comparatively large distance from the wall of a cavity confining the deuterium micro-explosion.

Thermonuclear microdetonation macron accelerator for impact ignition

It is proposed to replace the expensive ∼150 kJ petawatt laser as a means for the fast ignition of a highly compressed dense DT target by a small flyer plate propelled to high velocities by a thermonuclear microdetonation ignited at one end of a super-pinch. It appears that this can most efficiently be done with the previously proposed modification of the dense plasma focus device, adding a high voltage relativistic electron beam emitting diode inside the coaxial plasma focus discharge tube, igniting at the end of the plasma focus pinch column a thermonuclear detonation wave, propagating in the axial direction and accelerating at the end of the pinch a flyer plate to a velocity of 103 km s−1.

Fusion–fission–fusion fast ignition plasma focus

A crucial advancement in the problem for the controlled release of energy by nuclear fusion appears possible by an autocatalytic fusion–fission–fusion microexplosion, where the deuterium–tritium (DT) fusion reaction of a dense magnetized DT plasma placed inside a thin liner made up of U238, Th232 (perhaps B10) releases a sufficient number of 14 MeV fusion neutrons which by fission reactions in the liner implode the liner on the DT plasma. The liner implosion increases the DT plasma density and with it the neutron output accelerating the fast fission reactions. Following the fast fission assisted ignition, a thermonuclear detonation wave can propagate into unburnt DT to reach a high gain. The simplest way for the realization of this concept appears to be the dense plasma focus configuration, amended with a nested high voltage magnetically insulated transmission line for the heating of the DT. The large magnetic field needed for the α-particle entrapment of the DT fusion reaction is here generated by the thermomagnetic Nernst effect, amplifying the magnetic field of the plasma focus current sheet.

Autocatalytic Fusion-Fission Burn in the Focus of Two Magnetically Insulated Transmission Lines

A configuration made up of two nested magnetically insulated transmission lines, the inner one carrying a high voltage lower current - and the outer one a high current lower voltage - pulse, was in a previous communication proposed for the ignition of a magnetic field assisted thermonuclear detonation wave. Unlike the fast ignition concept, it does not require the compression of the DT fusion fuel to densities in excess of the solid state. Here I show that with the same configuration, but by surrounding the DT fusion fuel with a blanket of solid U238, Th232 or B10, the ignition of a thermonuclear detonation wave is possible with densities of the DT fuel less than solid state densities, because the DT fusion neutrons can make a sufficient number of fission reactions, greatly increasing the pressure in the blanket, compressing the DT to high densities, launching a magnetic field assisted thermonuclear detonation wave. This autocatalytic fusion-fission burn has the further advantage that it can burn natural uranium, thorium and even boron.

Ignition of a Thermonuclear Detonation Wave in the Focus of Two Magnetically Insulated Transmission Lines

For the ignition of a thermonuclear detonation wave assisted by a strong magnetic field, it is proposed to use two concentrically nested magnetically insulated transmission lines, the inner one transmitting a high- voltage lower-current-, and the outer one a high-current lower-voltage- electromagnetic pulse drawn from two Marx generators. The concept has the potential of large thermonuclear gains with an input energy conceivably as small as 105 J.

The possibility of using a low-tritium-content D-T mixture compressed with a high-power current pulse

The possibility of the propagation of a thermonuclear detonation wave in a deuterium pinch with a small (∼0.5%) tritium admixture is considered. The required pinch parameters and the necessary value of the current produced by a high-power pulsed current generator are estimated.

Laser Compression and Ignition of Z-Pinch Magnetized Dense Fusion Targets

Abstract With thin wire multimegampere shear flow stabilized fast z-pinch discharges, magnetic fields of hundreds of megagauss can be reached in the vicinity of the discharge channel. Then, if by laser-ablation-propulsion pieces of solid DT are simultaneously shot onto the discharge channel from several sides, the DT is compressed upon impact to high densities, with the magnetic field acting as a cushion to make the compression isentropic. The highly compressed and magnetized DT target can then be ignited at one point by a pulsed laser beam launching a thermonuclear detonation wave propagating along the discharge channel. Estimates indicate thermonuclear gains large in comparison to hohlraum targets.

Laser Ignition of an Isentropically Compressed Dense Z-Pinch

A dense z-pinch generated by a high voltage discharge over a corrugated helical sawtooth-shaped capillary tube with a solid DT core, is by shear flow stabilized against the m = 0 and m= 1 magnetohydrodynamic instabilities, and by rotational flow against the Rayleigh-Taylor instability. The shear-and rotational flow result from jet formation by the corrugated surface. A programmed voltage pulse can then isentropically compress the DT core to high densities, and if ignited at one end by a petawatt laser pulse, a thermonuclear detonation wave can be launched propagating along the z-pinch channel. The proposed z-pinch burn should also work without tritium as a thermonuclear detonation wave in deuterium.

Pulse Power Compression by Cutting a Dense Z-Pinch with a Laser Beam

Abstract A thin cut made through a z-pinch by an intense laser beam can become a magnetically insulated diode crossed by an intense ion beam. For larger cuts, the gap is crossed by an intense relativistic electron beam, stopped by magnetic bremsstrahlung resulting in a pointlike intense x-ray source. In either case, the impedance of the pinch discharge is increased, with the power delivered rising in the same pro-portion. A magnetically insulated cut is advantageous for three reasons: First, with the ion current com-parable to the Alfvèn ion current, the pinch instabilities are reduced. Second, with the energy deposit-ed into fast ions, a non-Maxwellian velocity distribution is established increasing〈σ ν〉 value for nuclear fusion reactions taking place in the pinch discharge. Third, in a high density z-pinch plasma, the intense ion beam can launch a thermonuclear detonation wave propagating along the pinch discharge channel. For larger cuts the soft x-rays produced by magnetic bremsstrahlung can be used to drive a thermonuclear hohlraum target. Finally, the proposed pulse power compression scheme permits to use a cheap low power d.c. source charging a magnetic storage coil delivering the magnetically stored energy to the pinch discharge load by an exploding wire opening switch.

Propagating Thermonuclear Burn by Laser Ignition of a Dense Z-Pinch

Abstract A linear pinch discharge above the Pease-Braginskii current and stabilized by axial shear flow can radiatively collapse to high densities. A thermonuclear detonation wave can then be launched from one end of the discharge channel by ignition with a powerful laser pulse. Axial shear flow stabilization may be realized by injecting a fast moving jet along the pinch discharge channel, possibly in combination with a frozen DT fiber positioned on the pinch axis.

The structure of detonation waves in supernovae

The theory of gaseous detonation is applied to thermonuclear detonation waves in supernovae. First, the two-temperature structure of strong shock waves in a dense degenerate plasma is considered. The ion-electron energy transfer rate is calculated for a plasma with arbitrary degeneracy of electrons. It is shown that the non-equilibrium heating of ions is unimportant for detonation. The steady planar one-dimensional structure of detonation waves both in C + O mixtures and in pure helium 4He is computed for densities from 106 to 3 × 109 g cm−3. The thickness of the detonation waves is obtained as a function of the initial density of the matter. The self-sustained detonation of helium is a Chapman–Jouguet detonation at all the densities considered. The self-sustained detonation of C + O mixtures is a Chapman–Jouguet detonation only at densities less than ∼ 107 g cm−3. At higher densities it is a pathological detonation with some velocity |$D^\ast \gt D_\text{CJ}$|⁠. Products of detonation are Fe-peak nuclei if the NSE state occurs in a detonated matter. The products are the intermediate mass nuclei Si, S, Ca, etc. in the case of incomplete detonation of C + O mixtures. The products are the partially unburned helium and Fe-peak nuclei with extremely small fractions of intermediate mass nuclei in the case of incomplete detonation of 4He. The thickness of detonation waves in C + O mixtures differs appreciably from that in helium.