"ÆÓÐÍÀË ÐÀÄÈÎÝËÅÊÒÐÎÍÈÊÈ"
"JOURNAL
OF RADIOELECTRONICS" N 1, 1998 |

V.A.Cherepenin^{1},
V.P.Shumilin^{2}

^{1}Institute of Radioengineering and
Electronics of Russian Academy of Sciences

^{2}High Energy Density Research Center, Russian Academy of
Sciences, IVTAN

Received December 10, 1998.

**INTRODUCTION**

Electromagnetic disturbances at explosions of charges of condensed high explosives
(HE), apparently, for the first time were found out by A.G.Ivanov in summer of 1938^{1}. In the subsequent years these effects were repeatedly
investigated in many laboratories of the world^{2-8}, and
the frequency range, in which it was possible to find out electromagnetic disturbances,
continuously extended toward the high frequencies. According to the results of these
experiments, it has appeared, in particular, that at frequencies up to megahertz (*f*£10^{6}Hz) these disturbances
represent themselves quasi-stationary electromagnetic fields, which quickly decrease
depending on distance from a point of explosion (~R^{-3}). At higher frequencies the microwave radiation itself was
found out, when the field decreases in inverse proportion to distance (~R^{-1}). We will be interested only in this high-frequency
radiation, the presence of which is not explained till now. Concerning low-frequency
disturbances see review^{7}.

Purely speaking, the set of the experimental facts, concerning the generation of
microwave radiation at explosions of condensed HE, is not big. In 1955 T.Takakura^{2}, working with small charges of lead azide (*M*=0.1¸0.4 g), has shown, that the radiation is registered on frequencies
up to 10^{8}Hz (more precisely, up to 90MHz). At *f*=190MHz
and 3.3GHz the radiation was not observed. At frequency 14MHz by direct measurements it
was shown, that the field decreases ~R^{-1}.
In 1959 B.Koch^{3} has published results of measurements of
radiation at frequency *f*=24.1MHz from the charge of tolite-hexogene (50/50) with
mass *M*=7.5·10^{2}g. From these data it follows, that
brightness temperature of radiation at this frequency is ~10^{15}°K. In 1965 W.H.Andersen and C.L.Long^{4}
measured a spectrum of radiation from the charge of tetryl *M*=20¸10^{3} g in mass over frequency range 4·10^{8}¸5·10^{8}Hz. It appears to be close
to line spectrum. In 1970 V.I.Pechkovskii and G.S.Kalchik^{8}
have registered radiation over frequency range *f*=7.8·10^{9}¸1.12·10^{10}Hz at a distance 300¸350 m apart from a place of explosion *M*=10^{4}g
of ammonium nitrate. The experiments were carried out under conditions of brightly
expressed channel effect. At last in 1993-1998 A.B.Prishchepenko and co-authors has
published a large cycle of work (see, for example,^{9-11}),
devoted to creation of electroexplosive sources of wide-band microwave radiation. It is
not excluded, that the registered radiation is connected not to presence of
radio-technical circuits, but is caused directly by HE. In such case it is possible
presumably to assert, that at explosions of HE charges (*M*=10^{2}¸10^{3}g) radiation with frequency up
to 1.5·10^{11}Hz is registered.

Thus, there is the some of the experimental facts, showing that at explosions of
condensed HE charges (as with a shell or without it) of small weight (*M*=10^{2}¸10^{4}g)
wide-band microwave radiation (*f*=10^{8}¸10^{11}Hz) is registered. The
intensity of this radiation much surpasses intensity of thermal radiation.

The present work is devoted to attempt to explain this phenomenon. The essence of the offered mechanism consists in following: during expansion of products of detonation a highly non-equilibrium medium is generated, oscillatory temperature of which can essentially exceed rotational one. Such medium is basically active from the point of view of generation and amplification of microwave radiation. As against laser active media, the frequency of collisions of molecules is about frequency of radiation, therefore the radiation will be wide-band. As an air behind a shock wave is strongly ionized, the radiation can leave the explosion zone boundaries only after the decrease of this ionization because of its expansion and instability of border of detonation products. As presence of a shell as a way of initiation of the charge can accelerate process of destruction of a conducting layer behind a shock wave.

**SPHERICAL EXPLOSION IN AIR**

For definition and by virtue of obvious advantages of symmetry we shall consider the explosion of a spherical condensed HE charge without a shell in air under normal conditions. We shall also assume, that the initiation comes true in the center of charge.

At the moment of an exit of detonation wave through a surface of charge, a shock wave is formed in air. This wave, gradually reducing the speed, is expanded into environment. The products of detonation during the expansion on the initial stage behave like a piston, which push a shock wave before itself. In later moment of time this piston ever more lags behind a shock wave and finally should stop. Estimations show, that in case of spherical explosion in air under normal conditions the size of area, occupied by the products of detonation, does not surpass approximately ten initial sizes of charge.

Experimental study of the initial stages of condensed spherical HE charges explosions^{12-14} has shown, that the speed of detonation products is well
described by a relationship

(1)

where R_{0} - initial radius of charge, D_{0}
- initial speed of a shock wave, *r*=R/R_{0}=1¸10,* n*=const (0<*n*<1). The quantities of D_{0} and *n* are experimentally determined for various HE.

Assuming detonation to be normal, we shall consider, that the substance behind the
detonation wave is characterized by Jouguet parameters. Thus, the distribution of state
variables over the charge in initial moment of time is extremely non-uniform, though it
does not affect the external dimensions of a charge. For further evolution of the
detonation products the rather important circumstance is that the substance was exposed to
heating up to Jouguet temperature (T_{H}) and is compressed
up to density r_{H}.

As estimations show, the moment of non-equilibrium appearance at expansion of
detonation products rather poorly depends on the specific law of cooling T(*r*), the
only important factor is that this cooling obeys the power law. Therefore, for many
practically important cases it is possible to consider, that this process is an adiabatic
one with a constant adiabatic index. At g=5/3

(2)

The initial speed of a shock wave in air can reach D_{0 }@10^{6}
cm/sec, that corresponds to Mach number @30. According to shock
adiabat for air^{15}, equilibrium temperature in this case
reaches 15 000°K and the electron concentration - n_{e}@10^{19}cm^{-3}.
The maximum electron concentration is near to a contact surface which separates the
detonation products and heated air behind a shock wave, while the effective thickness of a
conducting layer is much less than thickness of an air between a shock wave and a contact
surface^{16}. To make an estimation let us accept, that the
concentration is equilibrium one. Then from^{15} it is
possible to derive n_{e} as a function of a Mach number, or
dependence of critical frequency on *r*. For D_{0 }@10^{6}
cm/sec, *n*=2/3

5·10^{13} (3)

where *r*³1.3, and the frequency is expressed in Hz.
One can see, that at *r>*5 the microwave output of radiation from the zone of
explosion is possible. Actually, the process of destruction of a conducting layer behind a
shock wave is more complicated. The fact is, that the contact surface appears to be
unstable, especially in relation to small-scale disturbances^{17}.
This instability is well visible on numerous photos of an initial stage of the condensed
spherical HE charges explosion at *r*>5 (see, for example,^{14}).
Thus, the destruction of a conducting layer will occur faster and is non-uniform over the
surface of a shock wave.

**NON-EQUILIBRIUM IN DETONATION PRODUCTS**

Since the temperature is exactly the parameter determining the rates of various relaxation processes , we shall characterize explosion process by time

, (4)

while the initial charge radius, obviously, is proportional to weight of HE to power 1/3.

Though the characteristic time between collisions of molecules (t_{col}) at expansion grows proportionally with *r*^{4}, as translational degrees of freedom, as rotational ones will
be in equilibrium, since the initial frequency of collisions is rather high (~10^{13}Hz). The situation with oscillatory degrees of freedom is
different. As the resonant exchange of oscillatory quantums between molecules
(VV-relaxation) proceeds rather quickly, so Boltzmann’s distribution in energy of
oscillatory will not be disturb^{18}. However,
characteristic time of energy exchange between oscillatory and translational (and
rotational) degrees of freedom (VT- relaxation) grows exponentially with reduction of
temperature

(5)

where A and T_{VT} - constants depending on a type of
molecules. Therefore, a time moment inevitably comes, when t_{VT} will exceed t_{T}.
At further expansion the oscillatory temperature (T_{V})
already will not decrease. As estimations show, for typical HE it occurs at *r*=1.5¸2. Both weight and initial HE density influence a moment of
oscillatory temperature freezing only as a logarithmic function, while the reduction of T_{H} value (i.e. the use low-calorific HE) can essentially speed
up this process.

It is necessary to note also, that in case of strong gas dissociation, an inverse
process of recombination is a source of exited molecules, that can in turn increase the
time of VT-relaxation more than by a factor of 100^{19}.
Generally speaking, it concerns any chemical reaction, because during expansion the
endothermic channels of reactions "are blocked", while the remained exothermic
channels are sources of exited molecules.

One more important process, which equilibrium state is broken at expansion of
detonation products, is ionization. Since the temperature T_{H}
is not great, the equilibrium degree of ionization in an initial moment is small (~10^{-8}), that is, the basic process, in difference from^{20,21}, is ionization by heavy particles. In connection with
strong temperature dependence of ionization speed (~exp(-I/T), where I- the energy of
ionization) the non-equilibrium state is reached rather quickly (*r*~1) and at
further gas expansion the degree of ionization falls down only by recombination processes,
that is following the power law. So, for hexogene with initial density r_{0 }=1.66 g/cm^{3}
and *M*=1gramm the degree of ionization at *r*=5 will be ~2·10^{-11},
which corresponds to electron concentration ~10^{10}cm^{-3 }(*f*_{cr}~10^{9}Hz). The residual electron concentration grows up with
increase of T_{H} and falls down at growth of both *M*
and r_{0}.

(6)

Thus, the detonation products during the process of expanding represent themselves the medium, in which oscillatory temperature exceed rotational one by an order of magnitude, and the electron concentration is unusually high, despite of strong cooling of gas.

**RADIATIONAL INSTABILITY IN DETONATION PRODUCTS**

Non-equilibrium of medium is necessary, but not sufficient condition of amplification
and generation of electromagnetic radiation. Twiss^{22} has
shown, that for realization of negative absorption over some frequency range it is
necessary to comply simultaneously with two conditions:

(7)

and

(8)

where F(E) - function of energy (E) distribution, and Q_{w}(E)
- effective probability of stimulated radiation.

As over a microwave range of frequencies the energy of quantum of radiation is much
less than temperature, so the effect of negative absorption should be described in
classical approach. Such consideration was spent for one-dimension oscillators^{23-26}. It has appeared, that the ensemble of harmonic
oscillators, as well as in a quantum case, always absorbs energy, and for negative
absorption to take place in the monoenergetic oscillators medium they must necessarily be
unharmonic ones

(9)

For unharmonic oscillators with distribution function F(E) the negative absorption will be observed, if

(10)

across the energy interval

(11)

where n - frequency of collisions.

Actually the condition (10) is analogous to requirement of population inversion in a
quantum case. Usually two types of inversion are distinguished when considering the
molecular systems^{27}: oscillatory one, or complete, and
oscillatory- rotational, or partial. In our case, the complete inversion is not realized,
since the function of distribution in oscillatory degrees of freedom is Boltzmann’s.
Therefore, only the partial inversion is possible. The classical analogue of partial
inversion can be received by considering vibrating rotator, when function of distribution
in oscillatory (E_{V}) and rotational (E_{R})
energies are Boltzmann’s ones:

(12)

The oscillations of such rotator are non-harmonic ones. In this case

(13)

at T_{V}>T. As against effects, in which the basic
role plays oscillators unharmonism^{23-26}, this effect has
a kinetic character and at large frequencies of collisions is realized over a wide range
of radiation frequencies. Over the optical range of frequencies this effect was used for
creation of lasers^{28,29}.

Thus, in a considered case, the detonation products represent themselves an active medium, capable to amplify and generate the microwave radiation. Certainly, it is necessary, that this amplification exceeds the absorption in plasma of detonation products themselves and conducting layer behind a shock wave.

**CONCLUSION**

Within the framework of offered model a number of observable effects find its natural
explanation, in particular, the absence of high-frequency radiation at explosions of lead
azide charges^{2}. The fact is, that the detonation products
can represent themselves an active media only if the composition of detonation products is
rather rich in molecules with exited oscillatory degrees of freedom, and a great life
time. In a case of lead azide (PbN_{6}) there is an obvious
contradiction between the low heat of explosive transformation (and, hence, the low
temperature T_{H}) and large energy of oscillatory
excitation of molecules N_{2} (@3340°K).
For obtaining of wide-band microwave radiation the most optimum for composition are,
apparently, the secondary HE such as C_{a}H_{b}N_{g}O_{d}.

The well-known fact of radiation intensity increase at explosions of charges in shells can be explained by acceleration of destruction process of a conducting layer behind a shock wave. An essential moment is also the influence of both a shell and a way of charge initiation on the radiation pattern.

Thus, the considered mechanism of radiation will take effect after some delay from the moment of HE initiation, and this delay time is proportional to weight of HE to power 1/3. In absence of nonlinear effects the average frequency of radiation should decrease during a pulse. The important parameters, influencing the considered mechanism of radiation are: a type of HE and geometry of charge, existence of a shell, the way of initiation, external pressure.

In summary we would like to thank Dr. E.V.Chernykh and Prof. S.L.Ziglin for fruitful discussion of work.

**REFERENCES**

- A.G.Ivanov, Seismic-electrical effect of second kind,
*Transaction of USSR Academy of Sciences. Geography and Geophysics Series.*(Russian)*.*5:699 (1940). - T.Takakura, Radio noise radiated on the detonation of explosive,
*Publications of the Astronomical Society of Japan*. 7:210 (1955). - B.Koch, Emission d`ondes radioelectriques par des detonations,
*Academie des Sciences. comp. rend.*248:2173 (1959). - W.H.Andersen and C.L.Long, Electromagnetic radiation from detonating
solid explosives,
*J. Appl. Phys.*36:1494 (1965). - A.P.Boronin, V..A.Velmin, Yu.A.Medvedev, B.M.Stepanov, Experimental study
of electromagnetic field in an adjacent zone at explosions of condensed HE,
*Journ. of Appl. Mech. and Tech. Phys.*(Russian)*.*9:99 (1968). - A.P.Boronin, V.N.Kapinos, S.A.Krenev, About physical mechanism of
electromagnetic field generation by explosion of condensed HE charge. Experimental
research data,
*The Phys. of Combus. and Explos.*(Russian). - A.P.Boronin, V.N.Kapinos, S.A.Krenev, V.N.Mineev, About physical
mechanism of electromagnetic field generation by explosion of condensed HE charge. Review,
*The Phys. of Combus. and Explos.*(Russian). 26:110 (1990). - V.I.Pechkovskii, G.S.Kalchik, Attenuation of detonation under action of a
magnetic field, arising at explosion HE charges in shells,
*The Phys. of Combus. and Explos.*(Russian). 6:123 (1970). - A.B.Prishchepenko, V.V.Kiseljov and I.S.Kudimov, Radio frequency weapon
at the future battlefield,
*in:*”Electromagnetic Environments and Consequences. Proc. of the EUROEM 94 Int. Symp.”, D.J.Serafin, J.Ch.Bolomey, D.Dupouy ed., Gramat, France, I:266 (1995). - A.B.Prishchepenko, V.P.Zhitnikov, Microwave ammunitions: suum cuique,
*in:*”Ultra Wideband, Short-Pulse Electromagnetics 3. Proc. of the AMEREM 96 Int. Symp.” A.Stone, C.Baum and L.Carin ed., Plenum, New York, (In Press). - A.B.Prishchepenko, Invisible death of electronics,
*Soldier of Fortune.*(Russian). 3:45 (1996). - Yu.N.Ryabinin, I.I.Tamm, About similarity of air shock waves, formed by
HE charges,
*in:*”Physics of Explosion”, M.A.Sadovskii and A.F.Belyaev ed., USSR Academy of Sciences, Moscow, Russia, 5:71 (1956). - B.D.Ckristoforov, Air shock wave front parameters at explosion of PETN
and lead azide charges of different density,
*Journ. of Appl. Mech. and Tech. Phys.*(Russian)*.*2:175 (1961). - V.V.Adushkin, About formation of a shock wave and explosion products
flight in air.,
*Journ. of Appl. Mech. and Tech. Phys.*(Russian). 4:107 (1963). - N.M.Kuznetsov.”Air Thermodynamic Functions and Shock Adiabats at High Temperatures.” Mashinostroenie, Moscow (1965).
- B.S.Punkevich, B.M.Stepanov, Air electroconductivity behind shock wave
front at explosion of condenced HE,
*The Phys. of Combus. and Explos.*(Russian). 16:109 (1980). - S.I.Anisimov, Ia.B.Zeldovich, Rayleigh-Taylor instability of boundary
between detonation products and gas at spherical explosion,
*J. Tech. Phys. Lett.*(Russian). 3:1081 (1977). - E.V.Stupochenko, S.A.Losev, A.I.Osipov.”Relaxation Processes in Shock Waves”, Nauka, Moscow (1965).
- N.M.Kuznetsov, Oscillatory relaxation in recombinating extending gas,
*High Temperature Thermophysics*(Russian). 4:282 (1966). - Yu.P.Raizer, About residual ionization of gas, expanding in emptiness,
*J. Exper. And Theor Phys.*(Russian). 37:580 (1959). - N.M.Kuznetsov, Yu.P.Raizer, About electron recombination in plasma,
extending in emptiness,
*Journ. of Appl. Mech. and Tech. Phys.*(Russian). 6:10 (1965). - R.Q.Twiss, Radiation transfer and the possibility of negative absorption
in radio astronomy,
*Aust. J. Phys.*11:564 (1958). - A.V.Gaponov, Instability of a system of excited oscillators with respect
to electromagnetic perturbations,
*J. Exper. and Theor Phys.*(Russian). 39:326 (1960). - I.I.Sobelman, I.V.Tyutin, Stimulated radiating processes in quantum and
classical theories,
*Usp. Fiz. Nauk.*(Russian). 79:595 (1963). - A.V.Gaponov, M.I.Petelin, V.K.Yulpatov, Stimulated emission by exited
classical oscillators and its use in high-frequency electronics,
*Izv. Vuzov. Radiophysics.*(Russian). 10:1414 (1967). - V.M.Fain.”Quantum Radiophysics. v.1. Fotons and Nonlinear Media”. Sovetskoe radio, Moscow, (1972).
- M.S.Jijoev, V.G.Platonenko, R.V.Khokhlov, Chemical lasers,
*Usp. Fiz. Nauk.*(Russian). 100:641 (1970). - M.S.Jijoev, V.V.Korolev, V.N.Markov, V.G.Platonenko, R.V.Khokhlov,
Detonating gasdynamic laser,
*J. Exper. and Theor Phys. Lett.*(Russian). 14:73 (1971). - V.M.Marchenko, A.M.Prochorov, About an opportunity of creation of inverse
medium for lasers by means of explosion,
*J. Exper. and Theor Phys. Lett.*(Russian). 14:116 (1971).

*Authors:*

Cherepenin Vladimir Alekseevich, e-mail: cher@mail.cplire.ru

Shumilin Vladimir Pavlovich