Resonancia Schnuman y Cerebro

8/22/2019 Resonancia Schnuman y Cerebro

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

1 Introduction

Lately Nobelist L. Montagniers group has publishedthree articles deeply challenging the standard viewsabout genetic code and providing strong support forthe notion of water memory [13]. 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 (


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

At the same time it is known [812] 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 forms

one 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 in

review 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 systems breakdown parameters. In

other words, if the life (thermalization) time of cer-tain degrees of freedom interacting with field quantais larger than the systems 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 kT

has 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 Earths atmosphere betweendense ionized shell called ionosphere (at an altitude

of 100 km) and Earths surface, possesses the elec-tromagnetic resonant properties (Fig. 1 [16]). Hence,resonances of the spherical cavity Earths surface- ionosphere manifest themselves in electromagneticquasi-monochromatic signals that permanently presentnearby Earths surface and has certain impact ontothe Earths 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 Earths 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 the

atmosphere 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, Earthsmagnetic field strength HEarth, and concentration n of


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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 dense

ionized 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 Earths 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 Earths ionosphere versus altitude.

particles with mass M

fres =vA2l

, vA =HEarth

4M n, (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 of

HEarth 0.4 E, M 1.5 1023 g, n 105 cm3 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 Earths 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

Figure 2: Electromagnetic noise spectrum structure for mid-dle latitudes has a pronounced resonant structure (adapted

from [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 lightningsradiation 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, 2022], which isschematically shown in Fig. 1. The signals generated

via this mechanism are often referred to as pearls.The spectral dynamical characteristics of the pearlsand 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 [2325], that di-rectly correlate with predictions for IAR models [17]

and Alfven maser ones [22].Due to the fact that frequency bands of Alfven

maser 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 brain

biorhythms, 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-


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onators.

2 Types of relaxation oscillations in

Alfven 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 + 2Rw = 0, (2)

where

w =E E0

E0,

2v = 2vR

1 0recN0

1 + 2rec2R

nis

ln (m0)

(3)

and

2v R. (4)Here R and 2vR are characteristic frequency and

oscillations 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 Earths iono-sphere. These changes define reflection coefficients ofAlfven waves and, consequently, their attenuation in

the resonator under consideration; rec 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; = (k,vg),k is wave vector; vg is Alfven waves group velocity; 0corresponds to the steady state value of attenuationfactor

= |ln R()| /g, (5)where R() is a coefficient of Alfven wave reflectionfrom the magnetic mirrors, that lasts over ionosphere

and planet surface; g is propagation time of elec-tromagnetic signal along geomagnetic field line be-tween magneto-conjugated regions of the ionosphere;m = (m), (m) is normalized to unity Alfvenwave amplification for one pass along the radiation belt(RB), while coefficient equals to:

=4e20

menALW0, 0 =

v0c

, W0 =1

2mev

20, nA =

pLL

,

(6)

where v0 is typical velocity of particles, pL is the

ion plasma frequency of background plasma in mag-netosphere RB equatorial cross-section; L is gyro fre-quency in magnetosphere equatorial cross-section. Itshould be noted here, that the following approxima-tion for coefficient m is used for taking into account

the effect of the generated frequency sweep (drift):

m = 0 +mnis

nis, (7)

where 0 corresponds to equilibrium value of coefficient, which is obtained for the case of stationary solution

for 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 + w + w = 0, (8)

with initial conditions

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

where = 2R/2v, = 2v and w0 = [E(0) E0] /E0is a normalized initial energy of Alfven wave.

The advantages of such representation of the Alfvenwaves 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 +

2R2v

2v

t0

e2v(tt)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 e2v(tt), = 1/2v, (11)where u(t

t) is the unit Heaviside function. Ob-

viously, when v , equation (11) gains the -asymptotycs

f(t t) (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(2R/2v)t = w0e

t, (13)

where 1/ = 2v/2R is the time of w function viscos-

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

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


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

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

k1,2 =

2 1 1 4 , =

= , (14)

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

k1 = (1 + + . . . ) = (1 + ),k2 = (1 + . . . ) = (1 )/. (15)

In the case of > 1/4, which corresponds to R 2vR, or M < 4 (medium with a significant elastic-ity)

k1,2 =1

2 i, = 1

2

4 1. (16)Then the general solution satisfying the initial con-

ditions has the form

w = w01

k1 + k2

k2e

k1t k1ek2t

,

w0 =E(0) E0

E0. (17)

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

w = w0

(1 + )e(1+)t et

, 1, (18)

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

w = w0et/2 sin(t + )

sin , >

1

4, sin =

4 12

(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]et/2 sin(t + )sin

+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

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 their

explanations (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) =

=

t0

1

k2 k1

k2ek1(tt) k1ek2(tt)

(t)dt,

(21)

where, according to (17)

w(t) = w0

1

k2 k1 k2ek1t

k1ek2t

(22)

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

(t) = 0, (t)(t) = (t t) = (t t). (23)


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Let us consider the standard deviation

(w)2 =

t0

dt1

t0

dt2

2t=1

1

k2 k1

k2ek1(tti)

k1e

k2(tti)

(t1)(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 =

(k2 k1)2

k222k1

1 e2k1t

2k1k2k1 + k2

1 e(k1+k2)t

+

k212k2

1 e2k2t

.

(25)

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

(w)2t1/

= w2 = 2 w

, =kT

E0, (26)

we have

(k2 k1)3 =2(w/)

k22/2k1 2k1k2/(k1 + k2) + k21/2k2.

(27)

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

1

2k2=

2

(1 + ),1

k1 + k2= ,

1

2k1=

1

2(1 ).

(28)

In the case of > 1/4, when according to Eq. (16),k1,2 = /2 i and the relaxation character of dis-persion of Alfven wave energy to its equilibrium value

(26) becomes an oscillatory one (Fig. 4b):

(w)2 = 2w

1 et1 (1/

4 cos(2t + 3)

1 (1/4)cos3

,

(29)

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

= arctan

4 1, (30)and the thermodynamical function w/ by defini-tion is the thermal capacity CV, which in the simplestcase for plasma has the following form [26]:

CV =

w

V

= (Cideal)V +1

2

A

T3/2V1/2, A = const,

(31)

where Cideal is the thermal capacity of ideal gas.

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 following

form:

(E)2 = 2TE

T

1 et 1 (1/

4 cos(2t + 3)

1 (1/4)cos3

,

(32)

where T = kT.

Temporal behavior of average energy E (20) and

energy root-mean-square deviation

E1/2

(32) ofrelaxation 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 temperature. In combination with the measured frequency of os-cillations R it allows successively finding the values(at t = /), (for any t < = 1/) and m = 1/.

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 , relaxationtime (elasticity) of magnetoplasma medium andsettling time (viscosity) M of Maxwellian energydistribution (see Fig. 3).


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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= 2 103 [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 =2

R= 2

l

W0 2S0 , (34)

where R is the characteristic frequency of relaxationoscillations in Alfven resonator, = Bm/BL is themirror ratio for the Earths 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 Earthsradiation belt.

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

2LpL0m

= 1. (35)

If we take into account the experimental values forL 102 s1, nA 10 and 0 2 102 (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

m 5s1 fm 1.25 Hz. (36)

On the other hand, from (6), (35) and (36) it is nothard to find the value of W0

, which (if we assume

that nisL 3 102 cm3) would be equal

W0 102L

mnisL 102 s1 . (37)

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

pL =

4e2nisL/me,

which determines the characteristic time scale of theplasma oscillations.

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

TR =2

R= 2

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 cm2s1.

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

df

dt df

dnis dnis

dt = S0 df

dnis , (39)

where nis is the ionospheric plasma density, cm3.

According to [20], the numerical calculation ofdf /dnis for the calm morning gives the value 3 106 cm3 s1. On the other hand there are reasons tobelieve that under weak magnetic storminess the pro-tons with energy about 200 keV (and 102 cm1)flux density is S0 105 cm2s1. From this it followsthat the dynamic spectrum tilt is

df

dt S0 df

dnis 3 103

Hz s1

, (40)

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

Therefore we may conclude that the Polyakov-Rappoport-Trakhtengerts sweep-maser theory [1622]makes it possible to build a closed theory of genera-tion of a wide range of geomagnetic pulsations of thepearl type, which reside in the 0.110 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.


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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 diseases

mortality rate

As mentioned above, the theory of formation of thepearl 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

Figure 7: Frequency dependence of Alfven wave reflection coeffi-cient R from ionosphere containing IAR [17]: 1 - for solar activity

minimum, 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 ofR maximal values are indicatedwith arrows), where high rate generation of pearls takes place.

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

R() exp0 > 1, (41)where 0 = g is the logarithmic wave amplificationat a single passing of AR (Fig. 1a), R() is a coeffi-

cient of Alfven wave reflection from the magnetic mir-rors, that lasts over ionosphere and planet surface. Thepearl 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 ofpearls 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 pearlsappearance 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 Suns magnetic field we may concludeabout our principal knowledge of temporal evolutionof pearls appearance over the past 100 years, at theleast. Temporal dynamics of Suns magnetic field is

depicted in Fig. 8. Existence of strict anticorrelationbetween Suns magnetic field and terrestrial magneticfield3 (Y-component)[30] is seen from this figure, aswell.

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


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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 type

onto stability of the above brain biorhythms. If sucheffect really exists, then one would expect positive cor-relation between variation of geomagnetic pulsations ofpearl 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 Suns 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 malignant

neoplasm 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 Earths core are responsible for most magnetic variationsand, in particular, for the westward drift of magnetic featuresseen on the Earths 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 provide

in-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 mechanisms

of 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 [4244]. However, itmay be explained by the known and hard-to-removeeffect of the time shift in ice core data accompanying

any 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 [4244] 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 means

that 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 Earths atmosphere. In other words,cosmogenic nuclides (e.g. 10Be and 14C) are a kind


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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.

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 average

of 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 in a oscillatorycircuit on the depth h inside the body is decreasedfs times

fs(,h,,) = exp(h/), (42)


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where the path till absorption depends, according to[46], on the permeability ( 1) and conductivity ,and is defined as follows: = c(2)1/2. Since for < 106 s1 we have > 103 cm, for h 10 cm from(42) we obtain the value fs 1.

Taking into account the stated properties and the

known 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 cohorts

is 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 for

strong anticorrelation of the appearance of pearlsrelatively 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 ofSuns 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 pearlsappearance rate and temporal variations of death ratefrom various disruptions of brain diseases. The anti-correlation rate between temporal variations of Suns

magnetic 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 a

hypothesis 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 of6-10 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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