Can Resonant Oscillations of the Earth Ionosphere …V.D. Rusov et al. "Pearls" and Human Brain Biorhythm 3 i o no s hper e a t m o sp h e r e Earth radiation belt wave packet m a

Can Resonant Oscillations of the Earth Ionosphere Influence

the Human Brain Biorhythm?

V.D. Rusov1∗, K.A. Lukin2, T.N. Zelentsova1, E.P. Linnik1, M.E. Beglaryan1,V.P. Smolyar1, M. Filippov1 and B. Vachev3

1Department of Theoretical and Experimental Nuclear Physics,Odessa National Polytechnic University, Ukraine2Institute for Radiophysics and Electronics, NASU, Kharkov, Ukraine3Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria

Abstract

Within the frames of Alfven sweep maser theory the description of morphological features of geomagneticpulsations in the ionosphere with frequencies (0.1-10 Hz) in the vicinity of Schumann resonance (7.83 Hz) isobtained. It is shown that the related regular spectral shapes of geomagnetic pulsations in the ionospheredetermined by ”viscosity” and ”elasticity” of magneto-plasma medium that control the nonlinear relaxation ofenergy and deviation of Alfven wave energy around its equilibrium value. Due to the fact that the frequencybands of Alfven maser resonant structures practically coincide with the frequency band delta- and partiallytheta-rhythms of human brain, the problem of degree of possible impact of electromagnetic ”pearl” type resonantstructures (0.1-5 Hz) onto the brain bio-rhythms stability is discussed.

Keywords: Ionospheric Alfven resonator (IAR); ELF waves; cosmic rays; magnetobiological effect (MBE) incell; brain diseases statistics

PACS: 87.50.C-, 87.53.-j, 94.20.-y, 94.30.-d

1 Introduction

Lately Nobelist L. Montagnier’s group has publishedthree articles deeply challenging the standard viewsabout genetic code and providing strong support forthe notion of water memory [1–3]. In a series of del-icate experiments [1, 2] they demonstrated the possi-bility of the emission of low-frequency electromagneticExtremely Low Frequency (ELF) waves from bacte-rial DNA sequences and the apparent ability of thesewaves to organize nucleotides (the ”building” mate-rial of DNA) into new bacterial DNA by mediation ofstructures within water [4].

Without going into details of physical justificationof quantum-field interpretation of these results1, let usemphasize one significant experimental result of thisgroup. This result is related to stable detection of ELFwaves (<7 Hz) from bacterial DNA sequences. Obvi-ously, if the result is reproduced in similar experimentsof another research groups, the unique importance ofthis fact is difficult to overestimate in understandingof living matter essence.

First of all, it concerns not only research of drasti-

∗Cooresponding author e-mail: [email protected] Scientist reacted by sharp article ”Scorn over claim of

teleported DNA” [5].

cally new fundamental properties of spatial-temporalstructure of eukaryotic genome, but also refers tostudying of equally important issues that are related toexogenous nature of <7 Hz ELF waves impact directlyonto a human brain and its biorhythms.

It is well known that the brain neurons constitutedifferent types of networks that interact by meansof electrical signals. Neuron networks configurationscomprise electrical circuits of oscillatory type. Elec-trical oscillations with different frequencies correspondto different states of brain. These oscillations could bedetected by brain electroencephalogram.

Numerous investigations have shown that electri-cal oscillations of different frequencies dominate in ahealthy human being brain at its different states [6, 7].Transitions between brain activities happen not con-tinuously, but only in discrete steps, from one levelto another. The rest state corresponds to the stead-iest alpha-rhythm with frequencies laying within thefrequency band from 8 to 13 Hz. beta-rhythm withboundary frequencies 14-35 Hz corresponds to brainwork. The slowest oscillations at frequencies 0.5-4 Hzare typical for delta-rhythm which corresponds to deepsleep. At last, theta-rhythm with frequencies from 4to 7 Hz dominates in the brain if the state of nuisanceor danger appears.

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V.D. Rusov et al. ”Pearls” and Human Brain Biorhythm 2

At the same time it is known [8–12] that the weakmagnetic fields impact on biological systems is a sub-ject of the biophysics section called magnetobiology.It studies the biological reactions and mechanisms ofthe weak fields action. Magnetobiology is a part ofa general fundamental problem of the biological effi-ciency of the weak and ultraweak physicochemical fac-tors, which operate below the biological defense mech-anisms threshold, and so may be accumulated on asubcelluar level.

It is necessary to note here that there is no accept-able physical understanding of the way the weak mag-netic fields cause the living systems reaction [9] sofar, although it has been experimentally found thatsuch fields may change the biochemical reactions ratesharply in a resonance-like way [9, 13]. The physicalnature of this phenomenon is still unclear, and it formsone of the most important, if not a general, problemof magnetobiology which includes the co-called ”kTproblem”.

The problem consists in the fact that the weak mag-netic field energy (say, geomagnetic filed) of the sameorder as the kT heat energy is distributed over thevolume 12 orders of magnitude larger (which approx-imately corresponds to a cell size). In such form theproblem of the biological impact of the low-frequencymagnetic oscillations has two aspects[9]:

• what is a mechanism of the weak low-frequencymagnetic signal transformation that causes thechanges on the biochemical processes level of kTorder?

• what is a mechanism of such stability, i.e. howdo such small impacts not get lost on the heatdisturbances of kT order background?

Not going into details of this complex and funda-mental problem, the essence of which is expounded inreview by [9], let us note that in spite of the statedmagnetobiology difficulties, there are serious reasonsto believe that the main features of the magnetobio-logical effect are reliably established in numerous ex-periments and tests and are reproducible on differ-ent experimental models and under different magneticconditions. On the other hand, the answers to theabove-mentioned questions ”lie” in the nonequilibriumthermodynamics field. ”It is generally known thatmetabolism in living systems is a combination of pri-mary non-equilibrium processes. The origin and break-down of biophysical structures at time smaller than thetime of thermalization of all degrees of freedom in thesestructures provide a good example of systems that arefar from equilibrium where even weak field quanta canbe manifested in system’s breakdown parameters. In

other words, if the life (thermalization) time of cer-tain degrees of freedom interacting with field quantais larger than the system’s characteristic time of life,then such degrees of freedom exist in the absence oftemperature proper. Therefore, a comparison of theirenergy changes due to field quanta absorption with kThas no sense” [14]. The candidates for the solution ofthis problem today are the mechanism of the moleculequantum states interference for the idealized proteincavity [9, 14] and the mechanism of the molecular gy-roscope interference [9, 15].

Turning back to experiment, let us examine the pos-sible physical causes of the low-frequency geomagneticfields generation and the consequences of their impacton the eucaryotic cells in short.

It is well known that Earth’s atmosphere betweendense ionized shell called ionosphere (at an altitudeof 100 km) and Earth’s surface, possesses the elec-tromagnetic resonant properties (Fig. 1 [16]). Hence,resonances of the spherical cavity ”Earth’s surface- ionosphere” manifest themselves in electromagneticquasi-monochromatic signals that permanently presentnearby Earth’s surface and has certain impact ontothe Earth’s biosphere. Among resonances of this typein the frequency band between (0.1-10) Hz the mostknown and studied is the so called Schumann reso-nance at the frequency of 7.83 Hz. This resonanceis observed for electromagnetic waves with the wave-length exactly equal to the Earth’s circle. Schumannresonance has drawn attention of physicians practi-cally immediately after its discovery in connection withstudying of impact of electromagnetic radiation ontothe alpha-rhythms of human brain which lie within the8-13 Hz frequencies band.

Thunderstorms feed the Schumann resonator eter-nally. Initial frequency spectrum of electrical dis-charges (lightnings) during thunderstorms representspractically white noise. The resonant systems of near-Earth space filter out corresponding parts of the spec-trum which is shown in Fig. 2 [17].

Ionospheric Alfven Resonator (IAR) is being consid-ered along with Schumann resonator as a near-Earthresonant system, as well. In particular, with the help ofIAR it was possible to explain new resonant radiationin the frequency band of 0.1-10 Hz [18]. This radia-tion was discovered in 1985 and characterized by quasi-periodic modulation (within frequency range of 0.5-3Hz) of the oscillations. This modulation appears abovethe background noise electromagnetic spectrum of theatmosphere and has regular daily variation (Fig. 2). Itis not difficult to show [18], that within the frame ofIAR model the resonant frequency fres of these oscilla-tions is defined by ionosphere layer thickness l, Earth’smagnetic field strength HEarth, and concentration n of


ionoshpere

atmosphere

Earth

radiation belt

wave packet

mag

netic

fiel

d lin

e

solar protons

100 km

900 km

losscone

(a)

1000

300

100

102 104 106

(b)

height, km

electron density, cm-3

Figure 1: Earth and surrounding electromagnetic resonant ob-jects (adapted from [16, 17]). a) Air gap at the altitudes of 0-100 km is the global Schumann spherical resonator with 7.83 Hzresonant frequency; the altitude region of 100-1000 km is a denseionized shell (ionosphere). Inside its mass ionosphere Alfven res-onator with the first resonant frequency that varies in time withinthe limits of 0.5-3.0 Hz is located. Geomagnetic field lines lieabove the ionosphere and are shown in red. High-energy protonscross this tubes. This Geomagnetic field line rests upon magneto-conjugated regions of the Earth’s ionosphere which all togetherform the resonator of, so called, magnetosphere Alfven maserwhich generates ”pearl” type electromagnetic signals. Traffic di-agram for the particles in radiation belt is also depicted in thefigure. Particles with velocities being inside the loss cone (greenline), possess small transversal velocities and fall into dense layersof the atmosphere, whereas particles outside the loss cone (blueline with arrow) possess bigger transversal velocities and are cap-tured by geomagnetic tube-trap due to their reflections from themagnetic mirrors of the ionosphere; b) Density of charged par-ticles in plasma of Earth’s ionosphere versus altitude.

particles with mass M

fres =vA2l, vA =

HEarth√4πMn

, (1)

where vA is Alfven velocity. According to [18] the spec-trum structure shown in Fig. 2 is defined by resonantfrequency fres and its harmonics. For typical values ofHEarth ∼ 0.4 E, M ∼ 1.5 · 10−23 g, n ∼ 105 cm−3 andl ∼ 500 km this estimation gives fres ∼ 2 Hz. Ap-parently, this estimation is in a good agreement withexperimental frequencies estimations of the detectedradiations 0.5-3 Hz [18].

Here it is interesting to mention another impor-tant role of IAR properties in affecting dynamics oflarger scale resonator for Alfven waves: magneto-spheric resonator for Alfven waves Alfven Resonator(AR), formed by geomagnetic field line resting uponmagneto-conjugated regions of Earth’s surface. High-energy protons may cross geomagnetic field lines ofthe resonator and excite ultra-low frequency (ULF)electromagnetic oscillations practically in the samefrequency band: 0.2-5 Hz , due to maser effect forthe trapped protons and self-oscillatory mode of this

ampl

itud

e

0 10frequency, Hz

05.02.86, tMosc = 02.00

(a)

ampl

itud

e

0 10frequency, Hz

14.09.95, tMosc = 02.00

(b)

ampl

itud

e

0 10frequency, Hz

04.02.86, tMosc = 16.00

(c)

ampl

itud

e

0 10frequency, Hz

13.09.95, tMosc = 16.00

(d)

Figure 2: Electromagnetic noise spectrum structure for mid-dle latitudes has a pronounced resonant structure (adaptedfrom [17]). In the daytime (c) and d)) the spectrum has a peakassociated with Schuman resonance at 7.83 Hz, while at nighttime (a) and b)) electromagnetic noise produced by lightning’sradiation at the frequencies below Schumann resonance is filteredout by Ionosphere Alfven Resonator (IAR). In the years of solaractivity maximum the noise spectrum at night time is similar tothat of daytime.

resonator [19]. This generator was called as mag-netospheric Alfven maser [16, 17, 20–22], which isschematically shown in Fig. 1. The signals generatedvia this mechanism are often referred to as ”pearls”.The spectral dynamical characteristics of the ”pearls”and their temporal dependencies had been a mysteryfor researchers until recent times. a remarkable facthad been discovered recently consisting in the strongnegative correlation between intensity level of low-frequency resonant lines in the atmospheric noise ra-diation spectrum and solar activity [17], and, corre-spondingly, between intensity of resonant radiationsof ”pearl” type and solar activity [23–25], that di-rectly correlate with predictions for IAR models [17]and Alfven maser ones [22].

Due to the fact that frequency bands of Alfvenmaser resonances practically coincide with the fre-quency band of delta- and partially theta-rhythms ofhuman brain, the problem of possible impact of electro-magnetic fields of ”pearl” type onto stability of men-tioned brain bio-rhythms arises.

Thus, investigation of possible direct correlationbetween the values of average annual frequenciesof resonant electromagnetic signals of ”pearl” typeappearance, which have certain impact onto brainbiorhythms, and rate of average annual mortality be-cause of diseases due to various abnormal functioningof human brain was the subject of this paper. Let usdescribe the basic laws of the electromagnetic fieldsgeneration and oscillations in the abovementioned res-


onators.

2 Types of relaxation oscillations inAlfven maser

Below we present a brief analysis of solutions for theequation describing small oscillations of the wave en-ergy around its equilibrium state in the Alfven sweepmaser [20]:

w + 2vw + Ω2Rw = 0, (2)

where

w =E − E0

E0,

2v = 2vR

(1− γ0τrecχN0

1 + τ2recΩ

2R

· ∂

∂nisln (δmγ0)

)(3)

and

2v ΩR. (4)

Here ΩR and 2vR are characteristic frequency andoscillations decrement in Alfven resonator, respec-tively; w is the oscillation of the Alfven wave energywith respect to its equilibrium value E0. The latter isdefined for the case of no changes in the Earth’s iono-sphere. These changes define reflection coefficients ofAlfven waves and, consequently, their attenuation inthe resonator under consideration; τrec is character-istic recombination time in ionosphere plasma; N0 istotal number of fast particles in Geomagnetic field linehaving unit cross section at the ionosphere level; nis iselectron concentration in the ionosphere; χ = (~k,~vg),k is wave vector; vg is Alfven waves group velocity; γ0

corresponds to the steady state value of attenuationfactor

γ = |lnR(ω)| /τg, (5)

where R(ω) is a coefficient of Alfven wave reflectionfrom the magnetic mirrors, that lasts over ionosphereand planet surface; τg is propagation time of elec-tromagnetic signal along geomagnetic field line be-tween magneto-conjugated regions of the ionosphere;δm = φ(ωm)δ, φ(ωm) is normalized to unity Alfvenwave amplification for one pass along the radiation belt(RB), while coefficient δ equals to:

δ =4πe2β0

menAΩLW0, β0 =

v0

c, W0 =

1

2mev

20, nA =

ΩpL

ΩL,

(6)

where v0 is typical velocity of particles, ΩpL is theion plasma frequency of background plasma in mag-netosphere RB equatorial cross-section; ΩL is gyro fre-quency in magnetosphere equatorial cross-section. Itshould be noted here, that the following approxima-tion for coefficient δm is used for taking into account

the effect of the generated frequency sweep (drift):

δm = δ0 +∂δm∂nis

∆nis, (7)

where δ0 corresponds to equilibrium value of coefficientδ, which is obtained for the case of stationary solutionfor differential equations which describe the dynamicsof cyclotron instability in case of equilibrium electrondensity in the ionosphere.

It is convenient for analysis of typical forms of re-laxation oscillations in Alfven sweep-maser to rewritethe equations (2) in the following way:

w + λw + Γλw = 0, (8)

with initial conditions

w(0) = w0, w(0) = 0, (9)

where Γ = Ω2R/2v, λ = 2v and w0 = [E(0)− E0] /E0

is a normalized initial energy of Alfven wave.The advantages of such representation of the Alfven

waves energy relaxation oscillations become apparentduring the study of the physical reasons for the timeevolution of dispersion and, consequently, the morphol-ogy of such oscillations. For instance, it is easy to showthat the Polyakov-Rappoport-Trakhtengerts equation(2) is equivalent to the following integro-differentialequation:

w +

(Ω2R

2v

)· 2v

t∫0

e−2v(t−t′)w(t′)dt′ = 0, w(0) = w0.

(10)As follows from (10), the medium memory function

which characterizes its ”elastic” properties, has the fol-lowing form:

f(t− t′) = u(t− t′) · 2v · e−2v(t−t′), τλ = 1/2v, (11)

where u(t − t′) is the unit Heaviside function. Ob-viously, when v → ∞, equation (11) gains the δ-asymptotycs

f(t− t′)→ δ(t− t′), (12)

while the equation (10) and, consequently, equation(2) as well, turns into a trivial relaxation equation ofexponential type with the initial conditions:

w = w0e−(Ω2

R/2v)t = w0e−Γt, (13)

where 1/Γ = 2v/Ω2R is the time of w function ”viscos-

ity” relaxation to an equilibrium value w0, i.e. it is therelaxation time τM of the Maxwellian energy distribu-tion w to the equilibrium.

Willing to preserve the properties of ”viscosity” (τM )and ”quasi-elasiticity” (τλ) of the medium in equation


(2) let us hereinafter consider the equation (2) in theform of (8) with any finite τλ = 1/λ.

So the characteristic equation, corresponding to (8)has the roots

k1,2 =λ

2

(1∓

√1− 4η

), η =

Γ

λ= Γτλ, (14)

which are real when η < 1/4 so that the effective timeof the medium aftereffect τλ < τM/4, where τM = 1/Γis the time of the Maxwellian energy distribution set-tling. Particularly, in the case of a very short mediummemory (η 1) we have

k1 = λη(1 + η + . . . ) ∼= Γ(1 + η),

k2 = λ(1− η + . . . ) ∼= Γ(1− η)/η. (15)

In the case of η > 1/4, which corresponds to ΩR 2vR, or τM < 4τλ (medium with a significant ”elastic-ity”)

k1,2 =1

2λ∓ iω, ω =

1

2λ√

4η − 1. (16)

Then the general solution satisfying the initial con-ditions has the form

w = w01

k1 + k2

(k2e−k1t − k1e

−k2t),

w0 =E(0)− E0

E0. (17)

In the case of η < 1/4 the solution (17) takes on thefollowing form:

w ∼= w0

[(1 + η)e−Γ(1+η)t − ηe−λt

], η 1, (18)

which describes the exponential relaxation which isqualitatively different from e−Γt (a case of τλ = 0) onlyin the range 0 < t < τλ = 1/λ (Fig. 3a). Meanwhilefor the case of η > 1/4 the solution (17) describes anew kind of mode

w = w0e−λt/2 sin(ωt+ ϕ)

sinϕ, η >

1

4, sinϕ =

√4η − 1

2√η(19)

in a form of a attenuated periodic relaxation (Fig. 3b).Then the expression (19), allowing for (3) and (17),

may be represented in the following form

E(t) = [E(0)− E0]·e−λt/2 sin(ωt+ ϕ)

sinϕ+E0, E(0) > E,

(20)where E(t) is the Alfven waves energy.

It is known that the spectral analysis of experimentaldata corresponding to registration of magnetosphereradiation of ”pearl” type or, in other words, geomag-netic pulsations Pc1, allows one to reveal their inter-nal frequency structure [2], and the frequency inside

-Γte

w(t)w0

1

0 tτλ 1Γ(1+η)

1Γ

(a)

w(t)w0

1

0 t

(b)

- λte12

Figure 3: Exponential (a) and oscillatory (b) types of relax-ations of Alfven wave energy perturbations

of each ”pearl” (separate packet of Alfven waves) in-creases from its beginning to the end [17]. Quanti-tative estimates of ”pearl” parameters following fromthe theory above are in a good agreement with the re-lated experiments [17, 20]. Relying on that theory andexperiment correspondence we will show below howthe mentioned above morphological features find theirexplanations (within the framework of Alfven sweep-maser theory) on the basis of evolution of dampingperiodic oscillations (19) or (20) with taking into ac-count dispersion relaxation of Alfven wave energy toits equilibrium value.

3 Maxwell distribution and relax-ation of Alfven wave energy dis-persion toward equilibrium value

According to Eq. (17), deviation of Alfven wave energyfluctuation from average value is given by

∆w(t) = w(t)− w(t) =

=

t∫0

1

k2 − k1

(k2e−k1(t−t′) − k1e

−k2(t−t′))ξ(t′)dt′,

(21)

where, according to (17)

w(t) = w01

k2 − k1

(k2e−k1t − k1e

−k2t)

(22)

and ξ(t) is normalized Gaussian noise with the follow-ing moments:

ξ(t) = 0, ξ(t)ξ(t′) = φ(t− t′) = φτδ(t− t′). (23)


Let us consider the standard deviation

(∆w)2 =

t∫0

dt1

t∫0

dt2

2∏t=1

1

k2 − k1

(k2e−k1(t−ti)−

−k1e−k2(t−ti)

)ξ(t1)ξ(t2). (24)

Then, after integration (24) and taking into account(21) and (23) we obtain the following general expres-sion for dispersion of Alfven wave energy:

(∆w)2 =φτ

(k2 − k1)2

[k2

2

2k1

(1− e−2k1t

)−

− 2k1k2

k1 + k2

(1− e−(k1+k2)t

)+

k21

2k2

(1− e−2k2t

)].

(25)

Assuming that for t τM = 1/Γ the energy distri-bution of Alfven wave is relaxing to Maxwell distribu-tion [26, 27]:

(∆w)2∣∣∣t1/Γ

= w2 = θ2 · ∂w

∂θ, θ =

kT

E0, (26)

we have

φτ

(k2 − k1)3=

θ2(∂w/∂θ)

k22/2k1 − 2k1k2/(k1 + k2) + k2

1/2k2.

(27)

In the case of η 1 (τλ τM ) the dispersion re-laxation to its equilibrium value (26) is schematicallyshown in Fig. 4a. It is characterized by three relax-ation times:

1

2k2=τλ2

(1 + η),1

k1 + k2= τλ,

1

2k1=

1

2Γ(1− η).

(28)

In the case of η > 1/4, when according to Eq. (16),k1,2 = λ/2 ± iω and the relaxation character of dis-persion of Alfven wave energy to its equilibrium value(26) becomes an oscillatory one (Fig. 4b):

(∆w)2 = θ2∂w

∂θ·[1− e−λt 1− (1/

√4η cos(2ωt+ 3ϕ)

1− (1/√

4η) cos 3ϕ

],

(29)

where value ϕ is defined according to formula afterEq. (19)

ϕ = arctan√

4η − 1, (30)

and the thermodynamical function ∂w/∂θ by defini-tion is the thermal capacity CV , which in the simplestcase for plasma has the following form [26]:

CV =

(∂w

∂θ

)V

= (Cideal)V +1

2

A

T 3/2V 1/2, A = const,

(31)

where Cideal is the thermal capacity of ideal gas.

12Γ

(Δw)2

θ2 ∂w∂θ

0 τλ t

(a)

(b)

(Δw)2

θ2 ∂w∂θ

0 tπω

τλ

Figure 4: Relaxation of Alfven wave energy dispersion var(w) toequilibrium value for aperiodic (a) and oscillatory (b) characterof relaxation in the medium with memory.

Let us remind that the expression (29) taking intoaccount (3) and (26) can be presented in the followingform:

(∆E)2 = θ2T ·∂E

∂θT·[1− e−λt 1− (1/

√4η cos(2ωt+ 3ϕ)

1− (1/√

4η) cos 3ϕ

],

(32)

where θT = kT .

Temporal behavior of average energy E (20) and

energy root-mean-square deviation(∆E

)1/2(32) of

relaxation oscillations of Alfven waves in magneto-plasma medium (medium with memory) are presentedin Fig. 5.

It is worth noting here, that such approach opensup nontrivial possibility for experimental numericalestimations of some important parameters of Alfvensweep-maser relaxation oscillations. For instance, thelimit width of distribution (26) allows determining theplasma thermal capacity CV for the given temperatureθ. In combination with the measured frequency of os-cillations ΩR it allows successively finding the valuesλ(at t = π/ω), η (for any t < τλ = 1/λ) and τm = 1/Γ.

In other words, analysis of energy dispersion evolu-tion of Alfven sweep-maser relaxation oscillations al-lows finding experimentally (see Fig. 5) the values ofplasma thermal capacity CV , decrement λ, relaxationtime (”elasticity”) τλ of magnetoplasma medium andsettling time (”viscosity”) τM of Maxwellian energydistribution (see Fig. 3).


- λte12

πω

τλ

(ΔE)2 = ΘT ∂ΘT

∂E1 2

t0

E0

E

Figure 5: Oscillatory relaxation of Alfven wave average energy Eand its dispersion var(E) in magnetoplasma medium (mediumwith memory).

And finally, folowing [20], let us give some quanti-tative estimations. Accrording to [25], the recurrenceperiod of the elements in ”pearls” is about 50-300 s(Fig. 2), the bandwidth ∆f fits into the range 0.05-0.3 Hz, and the dynamic spectrum tilt is

df

dt∼= 2 · 10−3 [Hz]. (33)

In order to estimate the radiation parameters follow-ing from the sweep-maser theory [20], let us consider amagnetic flux tube on the morning side of a magneto-sphere2 at a distance of R ≈ 3REarth from the Earthcenter, where REarth is the Earth radius. In the frame-work of the sweep-maser theory it has been shown thatthe relaxation oscillations period, which characterizesthe recurrence period of the elements in pulsations ofthe ”pearl” type is

TR =2π

ΩR= 2π

√σ · l

W0 · δ · 2S0, (34)

where ΩR is the characteristic frequency of relaxationoscillations in Alfven resonator, σ = Bm/BL is themirror ratio for the Earth’s radiation belt, Bm is themagnetic field at the ends of the magnetic trap, BL is amagnetic field in equatorial section of magnetosphere,l is the effective length of a resonator, S0 is the equilib-rium precipitating protons flux density in the Earth’sradiation belt.

According to [20], the amplification curve φ(ωm)(see. (3)) reaches its maximum when

Ω2L

ΩpLβ0ωm∼= 1. (35)

If we take into account the experimental values forΩL ≈ 102 s−1, nA ≈ 10 and β0 ≈ 2 · 10−2 (for the

2Geomagnetic pulsations of ”pearl” type are known [25] toappear primarily on the morning side of magnetosphere at midlatitudes at magnetically calm times.

particles with energy W0 ≈ 200 keV ) and allow for (6)and (35), we find that

ωm ∼ 5s−1 ⇔ fm ∼ 1.25 Hz. (36)

On the other hand, from (6), (35) and (36) it is nothard to find the value of W0 · δ, which (if we assumethat nisL ≈ 3 · 102 cm−3) would be equal

W0δ ∼10Ω2

L

ωmnisL≈ 102

[s−1]. (37)

where the ionospheric plasma density nisL is definedby the so-called plasma frequency

ΩpL =√

4πe2nisL/me,

which determines the characteristic time scale of theplasma oscillations.

Consequently, taking into account (34), (37) and theexperimental data for σ = 27 and l ≈ R we derive

TR =2π

ΩR= 2π

104

S1/20

. (38)

The period TR obviously hits the experimentally ob-served range 50÷ 300 s with the experimentally justi-fied value S0 ∼ 105 cm−2s−1.

Let us pass on to the dynamic spectrum tilt estima-tion:

df

dt≈ df

dnis· dnisdt∼= χ · S0 ·

df

dnis, (39)

where nis is the ionospheric plasma density, cm−3.According to [20], the numerical calculation of

df/dnis for the calm morning gives the value ∼ 3 ·10−6 cm3 ·s−1. On the other hand there are reasons tobelieve that under weak magnetic storminess the pro-tons with energy about 200 keV (and χ ≈ 10−2 cm−1)flux density is S0 ∼ 105 cm−2s−1. From this it followsthat the dynamic spectrum tilt is

df

dt≈ χ · S0 ·

df

dnis∼ 3 · 10−3

[Hz · s−1

], (40)

which corresponds to the experimental data [25] witha satisfiable accuracy.

Therefore we may conclude that the Polyakov-Rappoport-Trakhtengerts sweep-maser theory [16–22]makes it possible to build a closed theory of genera-tion of a wide range of geomagnetic pulsations of the”pearl” type, which reside in the 0.1÷10 Hz band andare observed primarily at the mid latitudes under theconditions of a weak magnetic storminess on the morn-ing side of magnetosphere. In other words, it is shownthat all the morphological features of geomagnetic pul-sations of the ”pearl” type mentioned above find theiradequate explanation in the framework of the Alfvensweep-maser theory.


1960 1970 1980 1990Time (years)

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rly

sum

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the

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inde

x N

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Figure 6: Solar cycle (yellow) variations of geomagnetic pulsa-tions Pc1 (green) activity for about four (from 19th through 21st)cycles [25].

4 On connections between varia-tions of geomagnetic pulsations,solar cycles and brain diseasesmortality rate

As mentioned above, the theory of formation of the”pearl” wave packets (geomagnetic pulsations Pc1) inAlfven maser may help in solving another problem.This problem lies in the fact of strong inverse correla-tion between the appearance frequency of geomagneticpulsations Pc1 and 11-year solar cycle. It has beenfound by means of long-term observations that geo-magnetic pulsations Pc1 activity is more intense (byfactor of 10) during the periods of solar minima ratherthan in its maxima (Fig.6). Below we will try to clar-ify this dependency within the frame of Alfven masertheory.

Experimental observations of ionosphere have shownthat steepness of electron concentration profile at theattitudes ∼1000 km (see Fig. 1b) is considerably de-creasing in the years of solar activity maxima [28]. Thisfactor leads to decrease in the Alfven waves reflectioncoefficient from the upper layer of the IAR and, hence,to decrease in Q-factor of AR. Fig. 7 shows experimen-tal dependence of the reflection coefficient R of Alfvenwaves from IAR. It was obtained using ionosphere datafor the minimum and maximum of solar activity [28].One can see that appreciable decrease in the reflectioncoefficient R (and, therefore, worsening of the condi-tions for ”pearl” generation in magnetospheric Alfvenresonator (AR)) is observed for maximum of solar ac-tivity compared to its minimum. The explanation ofsuch behavior of the reflection coefficient R and, con-sequently, behavior of the ”pearl” generation rate israther straightforward and is given below.

The criterion for the wave generation in Alfven

1

2

0 1 2 3 4 f, Hz

1.0

0.8

0.6

0.4

0.2

R

Figure 7: Frequency dependence of Alfven wave reflection coeffi-cient R from ionosphere containing IAR [17]: 1 - for solar activityminimum, 2 - for solar activity maxim. Drop of plasma concen-tration at altitudes of 250-1000 km is much more pronounced inthe solar activity minimum. It leads to the greater value of re-flection coefficient R (regions of R maximal values are indicatedwith arrows), where high rate generation of ”pearls” takes place.

maser according to (5) has the form [16, 17]

R(ω) · exp Γ0 > 1, (41)

where Γ0 = γτg is the logarithmic wave amplificationat a single passing of AR (Fig. 1a), R(ω) is a coeffi-cient of Alfven wave reflection from the magnetic mir-rors, that lasts over ionosphere and planet surface. The”pearl” amplification changes little during the solar ac-tivity cycle and has its value considerably less thanunity. Whereas the maximal value of reflection coeffi-cient R in the typical for the ”pearls” frequency bandof 0.2-5 Hz changes considerably according to Fig. 7and decreases in the years of solar activity maxima.So, it is follows from the (41) that the temporal vari-ations of IAR Q-factor affect the appearance rate of”pearls” generation. In other words, reflection coeffi-cient R behavior clearly explains (via the criterion ofwave generation in Alfven maser (41)) the dynamicsof ”pearls” appearance rate, which, in turn, explainsthe reason for strong anticorrelation between ”pearls”appearance and solar activity (Fig. 6).

Using this dependence and having temporal evolu-tion of solar activity or, that the same, the tempo-ral evolution of Sun’s magnetic field we may concludeabout our principal knowledge of temporal evolutionof ”pearls” appearance over the past 100 years, at theleast. Temporal dynamics of Sun’s magnetic field isdepicted in Fig. 8. Existence of strict anticorrelationbetween Sun’s magnetic field and terrestrial magneticfield3 (Y-component)[30] is seen from this figure, aswell.

3Note that the strong (inverse) correlation between the tem-


Due to the fact that the frequency band of Alfvenmaser resonant structures practically coincides withthe frequency band of delta-rhythms and, partially,theta-rhythms of human brain (see Fig. 7), the ques-tion naturally arises about the rate of possible influ-ence of global geomagnetic pulsations of ”pearl” typeonto stability of the above brain biorhythms. If sucheffect really exists, then one would expect positive cor-relation between variation of geomagnetic pulsations of”pearl” type Pc1 in the frequency band of 0.1-5 Hz andthe death rate from disruption of brain diseases. Ob-viously, the choice in this case should concern only thecurrently incurable brain diseases so that their statis-tics were close to the real one and not being masked byintensive treatment. This fully applies to such diseasesas malignant neoplasm of brain [31]. Their temporaldynamics in West Germany [31] is shown in Fig. 8.It is of interest that for our purposes the male statis-tics of infectious diseases (incl. Tuberculosis) in France[32] also applicable, that reflects, apparently, featuresof local spatial-temporal dynamics of magnetic field inEurope.

It is easy to show, that degree of anti-correlationbetween temporal variations of Sun’s magnetic fieldor, that the same, degree of direct correlation betweenfrequency of ”pearls” appearance and the number ofdeaths from considered diseases is high enough. Thisresult is based on the experimental data on malignantneoplasm of brain [31], malignant brain tumor [36],brain lymphomas [37] and infectious diseases (incl. Tu-berculosis) [32]. In this way, according to Fig. 8, timearranged statistics of these diseases are lagging behindthe variations of the Solar and Earth magnetic fields22-27 years and 10-15 years respectively. This delayeffect on the one hand can be a consequence of thelong-time hidden disease incubation period, but on theother hand opens up possibilities for prediction (at thetime lag length) of behavior variations of indicated dis-eases by means of experimental observation of the ge-omagnetic field temporal variations.

It is interesting to note here that a strong corre-lation between the galactic cosmic ray variations andcancer mortality birth cohorts has been discovered re-

poral variations of magnetic flux in the tachocline zone and theEarth magnetic field (Y-component) are observed only for exper-imental data obtained at that observatories where the temporalvariations of declination (∂D/∂t) or the closely associated eastcomponent (∂Y/∂t) are directly proportional to the westwarddrift of magnetic features [29]. This condition is very importantfor understanding of physical nature of indicated above correla-tion, so far as it is known that just motions of the top layersof the Earth’s core are responsible for most magnetic variationsand, in particular, for the westward drift of magnetic featuresseen on the Earth’s surface on the decade time scale. Europeand Australia are geographical places, where this condition isfulfilled (see Fig. 2 in [29]).

cently [38, 39]. It was observed for population cohortsin five countries on the three continents. Previous ev-idence [39] has implicated a role for cosmic rays in USfemale cancer, involving a possible cross-generationalfoetal effect (grandmother effects). According to theassumption of the authors [38, 39], it may providein-sight into the exploration of the role of germ cellsas a possible target of this radiation and genetic orepigenetic sources of cancer predisposition that couldbe used to identify individuals carrying the radiationdamage. And the conclusion about the galactic cosmicrays as a direct physical cause of the cancer mortalitybirth cohorts is based on a similar dependence of thetotal cancer age-standardized incidence rates and cos-mic ray rigidity from geomagnetic latitude (see Fig. 8in [38]).

Not reducing the role of the physical mechanismsof radiation-induced effects formation and non-linearcell response in low doses of ionizing radiation (e.g.[40]),the study of which is a fundamental basis for thecontemporary microdosimetry [41], let us consider thepossibility of indirect impact of electromagnetic res-onance structures (in 0.1-5 Hz band) of ionosphericAlfven maser on the cells of the birth cohorts throughtheir direct impact on the germ cells of their parents.Fig. 8b,c shows a high level of inverse correlation be-tween the temporal variations of the solar magneticfield (or direct correlation between the ”pearls” ap-pearance frequency) and cancer mortality rate of birthcohorts.

Time lag between the inverse solar magnetic fieldand cancer mortality birth cohorts is ∼6 years for UK-data and ∼10 years for USA-data, as follows fromFig. 8b,c. At first sight it may seem to contradict the28-year lag between the galactic cosmic rays variationsand cancer mortality birth cohorts, established in thepaper by [38] basing on the data [42–44]. However, itmay be explained by the known and hard-to-removeeffect of the time shift in ice core data accompanyingany 10Be measurements (proxy of galactic cosmic rays)in ice cores of Greenland and Antarctica.On the otherhand, theoretical verification of the actual 10Be-data[45] and their comparison with the analogous data ob-tained from [42–44] indicates that the time lag betweenthe galactic cosmic rays variations and cancer mortal-ity birth cohorts is ∼6-10 years.

There is also another more trivial justification ofthe 10-year time lag on the Fig. 8c. The variationsof galactic cosmic rays are obviously a consequence oftheir modulation by the solar magnetic field. It meansthat magnetic fields of the solar wind deflect the pri-mary flux of charged cosmic particles, which leads toa reduction of cosmogenic nuclide (e.g. 10Be and 14C)production in the Earth’s atmosphere. In other words,cosmogenic nuclides (e.g. 10Be and 14C) are a kind


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rate in US(b)

Breast cancer mortality rate in UK(c)

Geomagnetic field(d) Malignant brain

tumors (>65years)(e)

Malignant neoplasm of brain(f)

Brain lymphoma(g) Infectious mortality rate(h)

Figure 8: Time evolution (a) the variations of magnetic flux at the bottom (tachocline zone) of the Sun convective zone (see Fig. 7fin [33]), (b) fractional change in female breast cancer mortality for birth cohort in US (see Fig. 3b in [34]), (c) fractional change infemale breast cancer mortality for birth cohort in UK (see Fig. 2b in [34]), (d) geomagnetic field secular variations (Y-component,nT/year) as observed at the Eskdalemuir observatory (England) [35], where the variations (∂Y/∂t) are directly proportional to thewestward drift of magnetic features, (e) Malignant brain tumor (brain stem) [36], (f) the number of deaths from ICD9 item n191Malignant neoplasm of brain [31], (g) Brain lymphoma incidences in US [37] and (h) the mortality rates from infectious diseases(incl. Tuberculosis) at ages 15-34 in France [32]. The curves (a) and (d) are smoothed by the sliding intervals of 5 and 11 years.

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-700

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e, x

104 a

tom

/g

10B

e, p

rom

ille

Figure 9: Long-term cosmic rays reconstruction (from [45]). Cal-culated (grey curve) and actual annual 10Be content in Greenlandice (dotted curve). Open circles represent the 8-year data fromAntarctica [44]. Red line represents the 33-year moving averageof the grey curve [45].

of a ”shadow” of galactic cosmic rays on the Earthplaying the role of a proxy for the solar magnetic vari-ability. Therefore the variations of the solar magneticfield and galactic cosmic rays (or 10Be-proxy) must in-versely coincide which visually demonstrates the ex-perimentally justified result of the 1-year lag between10Be and sunspot originally detected by Beer et al.[42]. After all, one could not expect anything else be-cause the galactic cosmic rays variations are caused bythe solar magnetic field variations and not vice versa.

Turning back to a direct physical cause of the cancermortality birth cohorts, it should be noted that it ispractically impossible to separate the possible radia-

tive effect on germ cells (according to [34]) from themagnetobiological effect induced by such electromag-netic radiation as ”pearls”, since:

a) electromagnetic radiation of the ”pearls” type isgenerated as a result of the protons (a dominantcomponent of the cosmic rays) passage throughthe Alfven maser resonator, which is a magneto-spheric magnetic flux tube resting upon the partsof ionosphere in the conjugate hemispheres of theEarth;

b) the intensity variations of electromagnetic radia-tion of the ”pearls” type – because of their origin– not only is correlated with the galactic cosmicrays variations, but also display a similar latitudedependence;

c) magnetic field of the ”pearls” can freely penetratethe human body just like any other magnetic field,because the human body tissues almost do not de-crease their intensity; indeed, the harmonic ampli-tude of the field with frequency ω in a oscillatorycircuit on the depth h inside the body is decreasedfs times

fs(ω, h, σ, µ) = exp(−h/δ), (42)


where the path till absorption δ depends, according to[46], on the permeability µ (∼ 1) and conductivity σ,and is defined as follows: δ = c(2πµωσ)−1/2. Since forω < 106 s−1 we have δ > 103 cm, for h 6 10 cm from(42) we obtain the value fs ∼ 1.

Taking into account the stated properties and theknown fact (e.g. [47, 48]) that the magnetic field maybe a kind of an agent that amplifies the original cause(chemical impact or exposure to ionizing radiation) ofthe carcinogenesis, we may assume that the magne-tobiological effect induced by the electromagnetic ra-diation of the ”pearls” type amplifies the cosmic raysradiative effect in the germ cells of the parents [34].

As one can easily see, the level of inverse correlationbetween the solar magnetic field variations (or directcorrelation between the frequency of the ”pearls” ap-pearance) and cancer mortality rate of birth cohortsis high enough. Also, according to Fig. 8c, the timeseries of this effect lag approximately 10 years behindthe temporal variations of the Earth magnetic field.On the one hand, such delay effect may be a conse-quence of the cross-generational foetal effect [34], andon the other hand, it makes it possible to predict thediscussed variations by experimental observation of thegeomagnetic field variations.

5 Conclusions

In the frames of Alfven maser theory the description ofmorphological features of relaxation oscillations in themode of geomagnetic pulsations of ”pearl” type (Pc1)in the ionosphere is obtained. These features are de-termined by ”viscosity” and ”elasticity” of magneto-plasma medium that control the nonlinear relaxationof energy and dispersion of Alfven wave energy to theequilibrium values.

On the basis of analysis of the ”pearls” generationcriterion in Alfven maser (41) the physical reasons forstrong anticorrelation of the appearance of ”pearls”relatively to solar activity are discussed. Obviously,that a priori knowledge of the temporal evolution of so-lar activity or, that the same, the temporal evolution ofSun’s magnetic field gives possibility to build the tem-poral evolution of ”pearls” appearance over the past100 years, at least. The latter opens up a possibilityfor studying of positive correlation between ”pearls”appearance rate and temporal variations of death ratefrom various disruptions of brain diseases. The anti-correlation rate between temporal variations of Sun’smagnetic field or, that the same, direct correlation ratebetween of ”pearls” appearance rate and the number ofdeaths from considered diseases was demonstrated tohave the high enough value. This result is supported bythe experimental data on malignant neoplasm of brain

[31], malignant brain tumor [36], brain lymphomas [37]and infectious diseases (incl. Tuberculosis) [32].

The analysis of the known correlation between thegalactic cosmic rays variations and cancer mortalitybirth cohorts observed for population cohorts in fivecountries on the three continents [34] let us suggest ahypothesis of a cooperative action of the cosmic raysand electromagnetic radiation of the ”pearls” type onthe germ cells of the parents which is responsible forthe so-called cross-generational foetal effect [34] witha lag of ∼6-10 years.

In conclusion, we have obtained results clearly show-ing the possible impact of electromagnetic resonant ra-diations generated in ionospheric Alfven maser ontostability of human brain biorhythms, such as delta-rhythms and, partially, theta-rhythms.

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Can Resonant Oscillations of the Earth Ionosphere …V.D. Rusov et al. "Pearls" and Human Brain Biorhythm 3 i o no s hper e a t m o sp h e r e Earth radiation belt wave packet m a

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