Can Resonant Oscillations of the Earth Ionosphere Influence The

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, Ukraine 2Institute for Radiophysics and Electronics, NASU, Kharkov, Ukraine 3Institute for Nuclear Research and Nuclear Energy, Soﬁa, Bulgaria

Abstract

Within the frames of Alfvénsweep maser theory the description of morphological features of geomagnetic pulsations in the ionosphere with frequencies (0.1-10 Hz) in the vicinity of Schumann resonance (7.83 Hz) is obtained. It is shown that the related regular spectral shapes of geomagnetic pulsations in the ionosphere determined by ”viscosity” and ”elasticity” of magneto-plasma medium that control the nonlinear relaxation of energy and deviation of Alfvénwave energy around its equilibrium value. Due to the fact that the frequency bands of Alfvénmaser resonant structures practically coincide with the frequency band delta- and partially theta-rhythms of human brain, the problem of degree of possible impact of electromagnetic ”pearl” type resonant structures (0.1-5 Hz) onto the brain bio-rhythms stability is discussed. Keywords: Ionospheric Alfvénresonator (IAR); ELF waves; cosmic rays; magnetobiological effect (MBE) in cell; brain diseases statistics PACS: 87.50.C-, 87.53.-j, 94.20.-y, 94.30.-d 1 Introduction cally new fundamental properties of spatial-temporal structure of eukaryotic genome, but also refers to Lately Nobelist L. Montagnier’s group has published studying of equally important issues that are related to three articles deeply challenging the standard views exogenous nature of <7 Hz ELF waves impact directly about genetic code and providing strong support for onto a human brain and its biorhythms. the notion of water memory [1–3]. In a series of del- It is well known that the brain neurons constitute icate experiments [1,2] they demonstrated the possi- different types of networks that interact by means bility of the emission of low-frequency electromagnetic of electrical signals. Neuron networks configurations Extremely Low Frequency (ELF) waves from bacte- comprise electrical circuits of oscillatory type. Elec- rial DNA sequences and the apparent ability of these trical oscillations with different frequencies correspond waves to organize nucleotides (the ”building” mate- to different states of brain. These oscillations could be rial of DNA) into new bacterial DNA by mediation of detected by brain electroencephalogram. structures within water [4]. Numerous investigations have shown that electri- Without going into details of physical justification cal oscillations of different frequencies dominate in a of quantum-field interpretation of these results1, let us arXiv:1208.4970v1 [physics.gen-ph] 23 Aug 2012 healthy human being brain at its different states [6,7]. emphasize one significant experimental result of this Transitions between brain activities happen not con- group. This result is related to stable detection of ELF tinuously, but only in discrete steps, from one level waves (<7 Hz) from bacterial DNA sequences. Obvi- to another. The rest state corresponds to the stead- ously, if the result is reproduced in similar experiments iest alpha-rhythm with frequencies laying within the of another research groups, the unique importance of frequency band from 8 to 13 Hz. beta-rhythm with this fact is difficult to overestimate in understanding boundary frequencies 14-35 Hz corresponds to brain of living matter essence. work. The slowest oscillations at frequencies 0.5-4 Hz First of all, it concerns not only research of drasti- are typical for delta-rhythm which corresponds to deep sleep. At last, theta-rhythm with frequencies from 4 ∗Cooresponding author e-mail: [email protected] 1New Scientist reacted by sharp article ”Scorn over claim of to 7 Hz dominates in the brain if the state of nuisance teleported DNA” [5]. or danger appears. V.D. Rusov et al. ”Pearls” and Human Brain Biorhythm 2

At the same time it is known [8–12] that the weak other words, if the life (thermalization) time of cer- magnetic fields impact on biological systems is a sub- tain degrees of freedom interacting with field quanta ject of the biophysics section called magnetobiology. is larger than the system’s characteristic time of life, It studies the biological reactions and mechanisms of then such degrees of freedom exist in the absence of the weak fields action. Magnetobiology is a part of temperature proper. Therefore, a comparison of their a general fundamental problem of the biological effi- energy changes due to field quanta absorption with kT ciency of the weak and ultraweak physicochemical fac- has no sense” [14]. The candidates for the solution of tors, which operate below the biological defense mech- this problem today are the mechanism of the molecule anisms threshold, and so may be accumulated on a quantum states interference for the idealized protein subcelluar level. cavity [9, 14] and the mechanism of the molecular gy- It is necessary to note here that there is no accept- roscope interference [9, 15]. able physical understanding of the way the weak mag- Turning back to experiment, let us examine the pos- netic fields cause the living systems reaction [9] so sible physical causes of the low-frequency geomagnetic far, although it has been experimentally found that fields generation and the consequences of their impact such fields may change the biochemical reactions rate on the eucaryotic cells in short. sharply in a resonance-like way [9, 13]. The physical It is well known that Earth’s atmosphere between nature of this phenomenon is still unclear, and it forms dense ionized shell called ionosphere (at an altitude one of the most important, if not a general, problem of 100 km) and Earth’s surface, possesses the elec- of magnetobiology which includes the co-called ”kT tromagnetic resonant properties (Fig.1[16]). Hence, problem”. resonances of the spherical cavity ”Earth’s surface The problem consists in the fact that the weak mag- - ionosphere” manifest themselves in electromagnetic netic field energy (say, geomagnetic filed) of the same quasi-monochromatic signals that permanently present order as the kT heat energy is distributed over the nearby Earth’s surface and has certain impact onto volume 12 orders of magnitude larger (which approx- the Earth’s biosphere. Among resonances of this type imately corresponds to a cell size). In such form the in the frequency band between (0.1-10) Hz the most problem of the biological impact of the low-frequency known and studied is the so called Schumann reso- magnetic oscillations has two aspects[9]: nance at the frequency of 7.83 Hz. This resonance is observed for electromagnetic waves with the wave- • what is a mechanism of the weak low-frequency length exactly equal to the Earth’s circle. Schumann magnetic signal transformation that causes the resonance has drawn attention of physicians practi- changes on the biochemical processes level of kT cally immediately after its discovery in connection with order? studying of impact of electromagnetic radiation onto the alpha-rhythms of human brain which lie within the • what is a mechanism of such stability, i.e. how 8-13 Hz frequencies band. do such small impacts not get lost on the heat disturbances of kT order background? Thunderstorms feed the Schumann resonator eter- nally. Initial frequency spectrum of electrical dis- Not going into details of this complex and funda- charges (lightnings) during thunderstorms represents mental problem, the essence of which is expounded in practically white noise. The resonant systems of near- review by [9], let us note that in spite of the stated Earth space filter out corresponding parts of the spec- magnetobiology difficulties, there are serious reasons trum which is shown in Fig.2[17]. to believe that the main features of the magnetobio- Ionospheric AlfvénResonator (IAR) is being consid- logical effect are reliably established in numerous ex- ered along with Schumann resonator as a near-Earth periments and tests and are reproducible on differ- resonant system, as well. In particular, with the help of ent experimental models and under different magnetic IAR it was possible to explain new resonant radiation conditions. On the other hand, the answers to the in the frequency band of 0.1-10 Hz [18]. This radia- above-mentioned questions ”lie” in the nonequilibrium tion was discovered in 1985 and characterized by quasi- thermodynamics field. ”It is generally known that periodic modulation (within frequency range of 0.5-3 metabolism in living systems is a combination of pri- Hz) of the oscillations. This modulation appears above mary non-equilibrium processes. The origin and break- the background noise electromagnetic spectrum of the down of biophysical structures at time smaller than the atmosphere and has regular daily variation (Fig.2). It time of thermalization of all degrees of freedom in these is not difficult to show [18], that within the frame of structures provide a good example of systems that are IAR model the resonant frequency fres of these oscilla- far from equilibrium where even weak field quanta can tions is defined by ionosphere layer thickness l, Earth’s be manifested in system’s breakdown parameters. In magnetic field strength HEarth, and concentration n of V.D. Rusov et al. ”Pearls” and Human Brain Biorhythm 3

(a) (b)

solar protons

loss cone (a) amplitude amplitude

radiation belt

wave packet

05.02.86, tMosc = 02.00 14.09.95, tMosc = 02.00

e height, km n i l 0 10 0 10 frequency, Hz frequency, Hz d l e i (b) f

c i 1000 t e shpe n iono re g a (c) (d) sp m 300 atmo here Earth 100

102 104 106 -3 amplitude

electron density, cm amplitude

100 km 900 km

04.02.86, tMosc = 16.00 13.09.95, tMosc = 16.00

0 frequency, Hz 10 0 frequency, Hz 10 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 Hz Figure 2: Electromagnetic noise spectrum structure for mid- resonant frequency; the altitude region of 100-1000 km is a dense dle latitudes has a pronounced resonant structure (adapted ionized shell (ionosphere). Inside its mass ionosphere Alfvénres- from [17]). In the daytime (c) and d)) the spectrum has a peak onator with the first resonant frequency that varies in time within associated with Schuman resonance at 7.83 Hz, while at night the limits of 0.5-3.0 Hz is located. Geomagnetic field lines lie time (a) and b)) electromagnetic noise produced by lightning’s above the ionosphere and are shown in red. High-energy protons radiation at the frequencies below Schumann resonance is filtered cross this tubes. This Geomagnetic field line rests upon magneto- out by Ionosphere AlfvénResonator (IAR). In the years of solar conjugated regions of the Earth’s ionosphere which all together activity maximum the noise spectrum at night time is similar to form the resonator of, so called, magnetosphere Alfvénmaser that of daytime. which generates ”pearl” type electromagnetic signals. Traffic di- agram for the particles in radiation belt is also depicted in the figure. Particles with velocities being inside the loss cone (green resonator [19]. This generator was called as mag- line), possess small transversal velocities and fall into dense layers of the atmosphere, whereas particles outside the loss cone (blue netospheric Alfvén maser [16, 17, 20–22], which is line with arrow) possess bigger transversal velocities and are cap- schematically shown in Fig.1. The signals generated tured by geomagnetic tube-trap due to their reflections from the via this mechanism are often referred to as ”pearls”. magnetic mirrors of the ionosphere; b) Density of charged par- The spectral dynamical characteristics of the ”pearls” ticles in plasma of Earth’s ionosphere versus altitude. and their temporal dependencies had been a mystery for researchers until recent times. a remarkable fact particles with mass M had been discovered recently consisting in the strong negative correlation between intensity level of low- v H f = A , v = √ Earth , (1) frequency resonant lines in the atmospheric noise ra- res 2l A 4πMn diation spectrum and solar activity [17], and, corre- where vA is Alfvénvelocity. According to [18] the spec- spondingly, between intensity of resonant radiations trum structure shown in Fig.2 is defined by resonant of ”pearl” type and solar activity [23–25], that di- frequency fres and its harmonics. For typical values of rectly correlate with predictions for IAR models [17] −23 5 −3 HEarth ∼ 0.4 E, M ∼ 1.5 · 10 g, n ∼ 10 cm and and Alfvénmaser ones [22]. l ∼ 500 km this estimation gives fres ∼ 2 Hz. Ap- Due to the fact that frequency bands of Alfvén parently, this estimation is in a good agreement with maser resonances practically coincide with the fre- experimental frequencies estimations of the detected quency band of delta- and partially theta-rhythms of radiations 0.5-3 Hz [18]. human brain, the problem of possible impact of electro- Here it is interesting to mention another impor- magnetic fields of ”pearl” type onto stability of men- tant role of IAR properties in affecting dynamics of tioned brain bio-rhythms arises. larger scale resonator for Alfvén waves: magneto- Thus, investigation of possible direct correlation spheric resonator for Alfvénwaves AlfvénResonator between the values of average annual frequencies (AR), formed by geomagnetic field line resting upon of resonant electromagnetic signals of ”pearl” type magneto-conjugated regions of Earth’s surface. High- appearance, which have certain impact onto brain energy protons may cross geomagnetic field lines of biorhythms, and rate of average annual mortality be- the resonator and excite ultra-low frequency (ULF) cause of diseases due to various abnormal functioning electromagnetic oscillations practically in the same of human brain was the subject of this paper. Let us frequency band: 0.2-5 Hz , due to maser effect for describe the basic laws of the electromagnetic fields the trapped protons and self-oscillatory mode of this generation and oscillations in the abovementioned res- V.D. Rusov et al. ”Pearls” and Human Brain Biorhythm 4 onators. the effect of the generated frequency sweep (drift):

∂δm δm = δ0 + ∆nis, (7) 2 Types of relaxation oscillations in ∂nis

Alfvénmaser where δ0 corresponds to equilibrium value of coefficient δ, which is obtained for the case of stationary solution Below we present a brief analysis of solutions for the for differential equations which describe the dynamics equation describing small oscillations of the wave en- of cyclotron instability in case of equilibrium electron ergy around its equilibrium state in the Alfvénsweep density in the ionosphere. maser [20]: It is convenient for analysis of typical forms of re- 2 ¨w+ 2v ˙w+ ΩRw = 0, (2) laxation oscillations in Alfvénsweep-maser to rewrite where the equations (2) in the following way: E − E ¨w+ λ ˙w+ Γλw = 0, (8) w = 0 , E0 with initial conditions γ0τrecχN0 ∂ 2v = 2vR 1 − 2 2 · ln (δmγ0) (3) 1 + τrecΩR ∂nis w(0) = w0, ˙w(0)= 0, (9)

2 and where Γ = ΩR/2v, λ = 2v and w0 = [E(0) − E0] /E0 2v ΩR. (4) is a normalized initial energy of Alfvénwave. The advantages of such representation of the Alfvén Here ΩR and 2vR are characteristic frequency and waves energy relaxation oscillations become apparent oscillations decrement in Alfvén resonator, respec- during the study of the physical reasons for the time tively; w is the oscillation of the Alfvénwave energy evolution of dispersion and, consequently, the morphol- with respect to its equilibrium value E0. The latter is ogy of such oscillations. For instance, it is easy to show defined for the case of no changes in the Earth’s iono- that the Polyakov-Rappoport-Trakhtengerts equation sphere. These changes define reflection coefficients of (2) is equivalent to the following integro-differential Alfvénwaves and, consequently, their attenuation in equation: the resonator under consideration; τrec is character- t istic recombination time in ionosphere plasma; N0 is 2 Ω Z 0 total number of fast particles in Geomagnetic field line ˙w+ R · 2v e−2v(t−t )w(t0)dt0 = 0, w(0) = w . 2v 0 having unit cross section at the ionosphere level; nis is 0 electron concentration in the ionosphere; χ = (~kˆ,~vg), (10) k is wave vector; vg is Alfvénwaves group velocity; γ0 As follows from (10), the medium memory function corresponds to the steady state value of attenuation which characterizes its ”elastic” properties, has the fol- factor lowing form:

γ = |ln R(ω)| /τg, (5) 0 0 −2v(t−t0) f(t − t ) = u(t − t ) · 2v · e , τλ = 1/2v, (11) where R(ω) is a coefficient of Alfvénwave reflection 0 from the magnetic mirrors, that lasts over ionosphere where u(t − t ) is the unit Heaviside function. Ob- viously, when v → ∞, equation (11) gains the δ- and planet surface; τg is propagation time of electromagnetic signal along geomagnetic field line be- asymptotycs tween magneto-conjugated regions of the ionosphere; f(t − t0) → δ(t − t0), (12) δm = φ(ωm)δ, φ(ωm) is normalized to unity Alfvén wave amplification for one pass along the radiation belt while the equation (10) and, consequently, equation (RB), while coefficient δ equals to: (2) as well, turns into a trivial relaxation equation of exponential type with the initial conditions: 4πe2β v 1 Ω δ = 0 , β = 0 ,W = m v2, n = pL , 0 0 e 0 A −(Ω2 /2v)t −Γt menAΩLW0 c 2 ΩL w = w0e R = w0e , (13) (6) 2 where v0 is typical velocity of particles, ΩpL is the where 1/Γ = 2v/ΩR is the time of w function ”viscos- ion plasma frequency of background plasma in mag- ity” relaxation to an equilibrium value w0, i.e. it is the netosphere RB equatorial cross-section; ΩL is gyro fre- relaxation time τM of the Maxwellian energy distribu- quency in magnetosphere equatorial cross-section. It tion w to the equilibrium. should be noted here, that the following approxima- Willing to preserve the properties of ”viscosity” (τM ) tion for coefficient δm is used for taking into account and ”quasi-elasiticity” (τλ) of the medium in equation V.D. Rusov et al. ”Pearls” and Human Brain Biorhythm 5

(2) let us hereinafter consider the equation (2) in the w(t) w0 (a) form of (8) with any finite τλ = 1/λ. 1 So the characteristic equation, corresponding to (8) has the roots -Γt λ Γ e k = 1 ∓ p1 − 4η , η = = Γτ , (14) 1,2 2 λ λ 1 0 τλ 1 t which are real when η < 1/4 so that the effective time Γ(1+η) Γ of the medium aftereffect τλ < τM /4, where τM = 1/Γ w(t) is the time of the Maxwellian energy distribution set- w0 1 (b) tling. Particularly, in the case of a very short medium memory (η 1) we have - 1 λt e 2 ∼ k1 = λη(1 + η + ... ) = Γ(1 + η), ∼ k2 = λ(1 − η + ... ) = Γ(1 − η)/η. (15) 0 t

In the case of η > 1/4, which corresponds to ΩR 2vR, or τM < 4τλ (medium with a significant ”elasticity”) Figure 3: Exponential (a) and oscillatory (b) types of relax- 1 1 k = λ ∓ iω, ω = λp4η − 1. (16) ations of Alfvénwave energy perturbations 1,2 2 2 Then the general solution satisfying the initial con- of each ”pearl” (separate packet of Alfvénwaves) in- ditions has the form creases from its beginning to the end [17]. Quanti- 1 −k1t −k2t tative estimates of ”pearl” parameters following from w = w0 k2e − k1e , k1 + k2 the theory above are in a good agreement with the re- E(0) − E0 lated experiments [17, 20]. Relying on that theory and w0 = . (17) E0 experiment correspondence we will show below how the mentioned above morphological features find their In the case of η < 1/4 the solution (17) takes on the explanations (within the framework of Alfvénsweep- following form: maser theory) on the basis of evolution of damping periodic oscillations (19) or (20) with taking into ac- ∼ h −Γ(1+η)t −λti w = w0 (1 + η)e − ηe , η 1, (18) count dispersion relaxation of Alfvénwave energy to its equilibrium value. which describes the exponential relaxation which is −Γt qualitatively different from e (a case of τλ = 0) only in the range 0 < t < τλ = 1/λ (Fig.3a). Meanwhile 3 Maxwell distribution and relax- for the case of η > 1/4 the solution (17) describes a ation of Alfvénwave energy dis- new kind of mode persion toward equilibrium value √ sin(ωt + ϕ) 1 4η − 1 According to Eq. (17), deviation of Alfvénwave energy w = w e−λt/2 , η > , sin ϕ = √ 0 sin ϕ 4 2 η fluctuation from average value is given by (19) ∆w(t) = w(t) − w(t) = in a form of a attenuated periodic relaxation (Fig.3b). t Then the expression (19), allowing for (3) and (17), Z 1 0 0 −k1(t−t ) −k2(t−t ) 0 0 = k2e − k1e ξ(t )dt , may be represented in the following form k2 − k1 0 sin(ωt + ϕ) (21) E(t) = [E(0) − E ]·e−λt/2 +E ,E(0) E, 0 sin ϕ 0 > (20) where, according to (17) 1 where E(t) is the Alfvénwaves energy. −k1t −k2t w(t) = w0 k2e − k1e (22) It is known that the spectral analysis of experimental k2 − k1 data corresponding to registration of magnetosphere and ξ(t) is normalized Gaussian noise with the follow- radiation of ”pearl” type or, in other words, geomag- ing moments: netic pulsations Pc1, allows one to reveal their inter- nal frequency structure [2], and the frequency inside ξ(t) = 0, ξ(t)ξ(t0) = φ(t − t0) = φτδ(t − t0). (23) V.D. Rusov et al. ”Pearls” and Human Brain Biorhythm 6

Let us consider the standard deviation (Δw)2 t t Z Z 2 1 2 ∂w 2 Y −k1(t−ti) θ (∆w) = dt1 dt2 k2e − ∂θ k2 − k1 0 0 t=1 −k2(t−ti) −k1e ξ(t1)ξ(t2). (24) (a) Then, after integration (24) and taking into account (21) and (23) we obtain the following general expres- 0 1 t sion for dispersion of Alfv´enwave energy: τλ 2Γ (Δw)2 φτ k2 (∆w)2 = 2 1 − e−2k1t − (k − k )2 2k 2 2 1 1 θ ∂w 2k k k2 ∂θ − 1 2 1 − e−(k1+k2)t + 1 1 − e−2k2t . k1 + k2 2k2 (25) (b)

Assuming that for t τM = 1/Γ the energy distribution of Alfv´enwave is relaxing to Maxwell distribution [26, 27]: 0 π τ t ω λ ∂w kT (∆w)2 = w2 = θ2 · , θ = , (26) t1/Γ ∂θ E0 Figure 4: Relaxation of Alfv´enwave energy dispersion var(w) to equilibrium value for aperiodic (a) and oscillatory (b) character we have of relaxation in the medium with memory.

φτ θ2(∂w/∂θ) 3 = 2 2 . Let us remind that the expression (29) taking into (k2 − k1) k2/2k1 − 2k1k2/(k1 + k2) + k1/2k2 (27) account (3) and (26) can be presented in the following form: In the case of η 1 (τλ τM ) the dispersion relaxation to its equilibrium value (26) is schematically √ 2 2 ∂E −λt 1 − (1/ 4η cos(2ωt + 3ϕ) shown in Fig.4a. It is characterized by three relax- (∆E) = θT · · 1 − e √ , ∂θT 1 − (1/ 4η) cos 3ϕ ation times: (32) 1 τλ 1 1 1 where θT = kT . = (1 + η), = τλ, = (1 − η). 2k2 2 k1 + k2 2k1 2Γ Temporal behavior of average energy E (20) and 1/2 (28) energy root-mean-square deviation ∆E (32) of In the case of η > 1/4, when according to Eq. (16), relaxation oscillations of Alfvén waves in magneto- k1,2 = λ/2 ± iω and the relaxation character of dis- plasma medium (medium with memory) are presented persion of Alfvénwave energy to its equilibrium value in Fig.5. (26) becomes an oscillatory one (Fig.4b): It is worth noting here, that such approach opens √ up nontrivial possibility for experimental numerical ∂w 1 − (1/ 4η cos(2ωt + 3ϕ) (∆w)2 = θ2 · 1 − e−λt √ , estimations of some important parameters of Alfvén ∂θ 1 − (1/ 4η) cos 3ϕ sweep-maser relaxation oscillations. For instance, the (29) limit width of distribution (26) allows determining the where value ϕ is defined according to formula after plasma thermal capacity C for the given temperature Eq. (19) V θ. In combination with the measured frequency of os- ϕ = arctan p4η − 1, (30) cillations ΩR it allows successively finding the values and the thermodynamical function ∂w/∂θ by defini- λ(at t = π/ω), η (for any t < τλ = 1/λ) and τm = 1/Γ. tion is the thermal capacity CV , which in the simplest In other words, analysis of energy dispersion evolu- case for plasma has the following form [26]: tion of Alfvénsweep-maser relaxation oscillations allows finding experimentally (see Fig.5) the values of ∂w 1 A plasma thermal capacity C , decrement λ, relaxation C = = (C ) + ,A = const, V V ideal V 3/2 1/2 ∂θ V 2 T V time (”elasticity”) τλ of magnetoplasma medium and (31) settling time (”viscosity”) τM of Maxwellian energy where Cideal is the thermal capacity of ideal gas. distribution (see Fig.3). V.D. Rusov et al. ”Pearls” and Human Brain Biorhythm 7

E particles with energy W0 ≈ 200 keV ) and allow for (6) and (35), we ﬁnd that - 1 λt e 2 −1 ωm ∼ 5s ⇔ fm ∼ 1.25 Hz. (36)

1 2 ∂E On the other hand, from (6), (35) and (36) it is not E0 (ΔE)2 = Θ T ∂Θ T hard to ﬁnd the value of W0 · δ, which (if we assume 2 −3 that nisL ≈ 3 · 10 cm ) would be equal 10Ω2 W δ ∼ L ≈ 102 s−1 . (37) π τ t 0 0 ω λ ωmnisL

where the ionospheric plasma density nisL is deﬁned Figure 5: Oscillatory relaxation of Alfv´enwave average energy E¯ by the so-called plasma frequency and its dispersion var(E) in magnetoplasma medium (medium p 2 with memory). ΩpL = 4πe nisL/me,

which determines the characteristic time scale of the And finally, folowing [20], let us give some quanti- plasma oscillations. tative estimations. Accrording to [25], the recurrence Consequently, taking into account (34), (37) and the period of the elements in ”pearls” is about 50-300 s experimental data for σ = 27 and l ≈ R we derive (Fig.2), the bandwidth ∆ f fits into the range 0.05- 0.3 Hz, and the dynamic spectrum tilt is 2π 104 T = = 2π . (38) R 1/2 ΩR df S0 =∼ 2 · 10−3 [Hz]. (33) dt The period TR obviously hits the experimentally ob- In order to estimate the radiation parameters follow- served range 50 ÷ 300 s with the experimentally justi- 5 −2 −1 ing from the sweep-maser theory [20], let us consider a fied value S0 ∼ 10 cm s . magnetic flux tube on the morning side of a magneto- Let us pass on to the dynamic spectrum tilt estima- sphere2 at a distance of R ≈ 3R from the Earth tion: Earth df df dn df center, where R is the Earth radius. In the frame- ≈ · is =∼ χ · S · , (39) Earth dt dn dt 0 dn work of the sweep-maser theory it has been shown that is is −3 the relaxation oscillations period, which characterizes where nis is the ionospheric plasma density, cm . the recurrence period of the elements in pulsations of According to [20], the numerical calculation of the ”pearl” type is df/dnis for the calm morning gives the value ∼ 3 · 10−6 cm3 ·s−1. On the other hand there are reasons to r 2π σ · l believe that under weak magnetic storminess the pro- TR = = 2π , (34) −2 −1 ΩR W0 · δ · 2S0 tons with energy about 200 keV (and χ ≈ 10 cm ) flux density is S ∼ 105 cm−2s−1. From this it follows where Ω is the characteristic frequency of relaxation 0 R that the dynamic spectrum tilt is oscillations in Alfvénresonator, σ = Bm/BL is the mirror ratio for the Earth’s radiation belt, Bm is the df df −3 −1 ≈ χ · S0 · ∼ 3 · 10 Hz · s , (40) magnetic field at the ends of the magnetic trap, BL is a dt dnis magnetic field in equatorial section of magnetosphere, which corresponds to the experimental data [25] with l is the effective length of a resonator, S0 is the equilibrium precipitating protons flux density in the Earth’s a satisfiable accuracy. radiation belt. Therefore we may conclude that the Polyakov- Rappoport-Trakhtengerts sweep-maser theory [16–22] According to [20], the amplification curve φ(ωm) (see. (3)) reaches its maximum when makes it possible to build a closed theory of generation of a wide range of geomagnetic pulsations of the 2 ”pearl” type, which reside in the 0.1÷10 Hz band and ΩL ∼ = 1. (35) are observed primarily at the mid latitudes under the ΩpLβ0ωm conditions of a weak magnetic storminess on the morn- If we take into account the experimental values for ing side of magnetosphere. In other words, it is shown 2 −1 −2 ΩL ≈ 10 s , nA ≈ 10 and β0 ≈ 2 · 10 (for the that all the morphological features of geomagnetic pulsations of the ”pearl” type mentioned above find their 2Geomagnetic pulsations of ”pearl” type are known [25] to appear primarily on the morning side of magnetosphere at mid adequate explanation in the framework of the Alfvén latitudes at magnetically calm times. sweep-maser theory. V.D. Rusov et al. ”Pearls” and Human Brain Biorhythm 8

0 R 1.0 200 1 Sunspot number W 2000 150 0.8 Pc1 2

100 0.6 W 4000 50 Yearly sum of the Pc1 index N Yearly 0.4 19 20 21 22 0 1960 1970 1980 1990 Time (years) 0.2

Figure 6: Solar cycle (yellow) variations of geomagnetic pulsa- th st tions Pc1 (green) activity for about four (from 19 through 21 ) 0 1 2 3 4 f, Hz cycles [25].

Figure 7: Frequency dependence of Alfvénwave reflection coefficient R from ionosphere containing IAR [17]: 1 - for solar activity 4 On connections between varia- minimum, 2 - for solar activity maxim. Drop of plasma concentration at altitudes of 250-1000 km is much more pronounced in tions of geomagnetic pulsations, the solar activity minimum. It leads to the greater value of re- solar cycles and brain diseases flection coefficient R (regions of R maximal values are indicated with arrows), where high rate generation of ”pearls” takes place. mortality rate maser according to (5) has the form [16, 17] As mentioned above, the theory of formation of the ”pearl” wave packets (geomagnetic pulsations Pc1) in R(ω) · exp Γ0 > 1, (41) Alfvénmaser may help in solving another problem. where Γ0 = γτg is the logarithmic wave amplification This problem lies in the fact of strong inverse correla- at a single passing of AR (Fig.1a), R(ω) is a coeffi- tion between the appearance frequency of geomagnetic cient of Alfvénwave reflection from the magnetic mir- pulsations Pc1 and 11-year solar cycle. It has been rors, that lasts over ionosphere and planet surface. The found by means of long-term observations that geo- ”pearl” amplification changes little during the solar ac- magnetic pulsations Pc1 activity is more intense (by tivity cycle and has its value considerably less than factor of 10) during the periods of solar minima rather unity. Whereas the maximal value of reflection coeffi- than in its maxima (Fig.6). Below we will try to clar- cient R in the typical for the ”pearls” frequency band ify this dependency within the frame of Alfvénmaser of 0.2-5 Hz changes considerably according to Fig.7 theory. and decreases in the years of solar activity maxima. Experimental observations of ionosphere have shown So, it is follows from the (41) that the temporal vari- that steepness of electron concentration profile at the ations of IAR Q-factor affect the appearance rate of attitudes ∼1000 km (see Fig.1b) is considerably de- ”pearls” generation. In other words, reflection coeffi- creasing in the years of solar activity maxima [28]. This cient R behavior clearly explains (via the criterion of factor leads to decrease in the Alfvénwaves reflection wave generation in Alfvénmaser (41)) the dynamics coefficient from the upper layer of the IAR and, hence, of ”pearls” appearance rate, which, in turn, explains to decrease in Q-factor of AR. Fig.7 shows experimen- the reason for strong anticorrelation between ”pearls” tal dependence of the reflection coefficient R of Alfvén appearance and solar activity (Fig.6). waves from IAR. It was obtained using ionosphere data Using this dependence and having temporal evolu- for the minimum and maximum of solar activity [28]. tion of solar activity or, that the same, the tempo- One can see that appreciable decrease in the reflection ral evolution of Sun’s magnetic field we may conclude coefficient R (and, therefore, worsening of the condi- about our principal knowledge of temporal evolution tions for ”pearl” generation in magnetospheric Alfvén of ”pearls” appearance over the past 100 years, at the resonator (AR)) is observed for maximum of solar ac- least. Temporal dynamics of Sun’s magnetic field is tivity compared to its minimum. The explanation of depicted in Fig.8. Existence of strict anticorrelation such behavior of the reflection coefficient R and, con- between Sun’s magnetic field and terrestrial magnetic sequently, behavior of the ”pearl” generation rate is field3 (Y-component)[30] is seen from this figure, as rather straightforward and is given below. well. The criterion for the wave generation in Alfvén 3Note that the strong (inverse) correlation between the tem- V.D. Rusov et al. ”Pearls” and Human Brain Biorhythm 9

Due to the fact that the frequency band of Alfvén cently [38, 39]. It was observed for population cohorts maser resonant structures practically coincides with in five countries on the three continents. Previous ev- the frequency band of delta-rhythms and, partially, idence [39] has implicated a role for cosmic rays in US theta-rhythms of human brain (see Fig.7), the ques- female cancer, involving a possible cross-generational tion naturally arises about the rate of possible influ- foetal effect (grandmother effects). According to the ence of global geomagnetic pulsations of ”pearl” type assumption of the authors [38, 39], it may provide onto stability of the above brain biorhythms. If such in-sight into the exploration of the role of germ cells effect really exists, then one would expect positive cor- as a possible target of this radiation and genetic or relation between variation of geomagnetic pulsations of epigenetic sources of cancer predisposition that could ”pearl” type Pc1 in the frequency band of 0.1-5 Hz and be used to identify individuals carrying the radiation the death rate from disruption of brain diseases. Ob- damage. And the conclusion about the galactic cosmic viously, the choice in this case should concern only the rays as a direct physical cause of the cancer mortality currently incurable brain diseases so that their statis- birth cohorts is based on a similar dependence of the tics were close to the real one and not being masked by total cancer age-standardized incidence rates and cos- intensive treatment. This fully applies to such diseases mic ray rigidity from geomagnetic latitude (see Fig. 8 as malignant neoplasm of brain [31]. Their temporal in [38]). dynamics in West Germany [31] is shown in Fig.8. Not reducing the role of the physical mechanisms It is of interest that for our purposes the male statis- of radiation-induced effects formation and non-linear tics of infectious diseases (incl. Tuberculosis) in France cell response in low doses of ionizing radiation (e.g. [32] also applicable, that reflects, apparently, features [40]),the study of which is a fundamental basis for the of local spatial-temporal dynamics of magnetic field in contemporary microdosimetry [41], let us consider the Europe. possibility of indirect impact of electromagnetic res- It is easy to show, that degree of anti-correlation onance structures (in 0.1-5 Hz band) of ionospheric between temporal variations of Sun’s magnetic field Alfvénmaser on the cells of the birth cohorts through or, that the same, degree of direct correlation between their direct impact on the germ cells of their parents. frequency of ”pearls” appearance and the number of Fig.8b,c shows a high level of inverse correlation be- deaths from considered diseases is high enough. This tween the temporal variations of the solar magnetic result is based on the experimental data on malignant field (or direct correlation between the ”pearls” ap- neoplasm of brain [31], malignant brain tumor [36], pearance frequency) and cancer mortality rate of birth brain lymphomas [37] and infectious diseases (incl. Tu- cohorts. berculosis) [32]. In this way, according to Fig.8, time Time lag between the inverse solar magnetic field arranged statistics of these diseases are lagging behind and cancer mortality birth cohorts is ∼6 years for UK- the variations of the Solar and Earth magnetic fields data and ∼10 years for USA-data, as follows from 22-27 years and 10-15 years respectively. This delay Fig.8b,c. At first sight it may seem to contradict the effect on the one hand can be a consequence of the 28-year lag between the galactic cosmic rays variations long-time hidden disease incubation period, but on the and cancer mortality birth cohorts, established in the other hand opens up possibilities for prediction (at the paper by [38] basing on the data [42–44]. However, it time lag length) of behavior variations of indicated dis- may be explained by the known and hard-to-remove eases by means of experimental observation of the ge- effect of the time shift in ice core data accompanying omagnetic field temporal variations. any 10Be measurements (proxy of galactic cosmic rays) It is interesting to note here that a strong corre- in ice cores of Greenland and Antarctica.On the other 10 lation between the galactic cosmic ray variations and hand, theoretical verification of the actual Be-data cancer mortality birth cohorts has been discovered re- [45] and their comparison with the analogous data obtained from [42–44] indicates that the time lag between poral variations of magnetic flux in the tachocline zone and the the galactic cosmic rays variations and cancer mortal- Earth magnetic field (Y-component) are observed only for exper- ity birth cohorts is ∼6-10 years. imental data obtained at that observatories where the temporal There is also another more trivial justification of variations of declination (∂D/∂t) or the closely associated east the 10-year time lag on the Fig.8c. The variations component (∂Y/∂t) are directly proportional to the westward drift of magnetic features [29]. This condition is very important of galactic cosmic rays are obviously a consequence of for understanding of physical nature of indicated above correla- their modulation by the solar magnetic field. It means tion, so far as it is known that just motions of the top layers that magnetic fields of the solar wind deflect the pri- of the Earth’s core are responsible for most magnetic variations mary flux of charged cosmic particles, which leads to and, in particular, for the westward drift of magnetic features a reduction of cosmogenic nuclide (e.g. 10Be and 14C) seen on the Earth’s surface on the decade time scale. Europe and Australia are geographical places, where this condition is production in the Earth’s atmosphere. In other words, fulfilled (see Fig. 2 in [29]). cosmogenic nuclides (e.g. 10Be and 14C) are a kind V.D. Rusov et al. ”Pearls” and Human Brain Biorhythm 10

1 900 1 920 1 940 1 960 1 980 2 000 2 020 107 0 4 1,2 0,3 14

6 100 3,5 0,2 10 50 3 1 12 0,1 ? 3 105 Mx 100 23 0 10 0,8 50 2,5 104 −0,1 150 8 0,6 2 −0,2 103 (a) Solar magnetic flux 200 (b) Breast cancer mortality rate in US 6 −0,3 0 1,5 (c) Breast cancer mortality 0,4 102 rate in UK Solar magnetic fl ux, x10 −0,4 250 (d) Geomagnetic field (e) Malignant brain 4 1 tumors (>65years) Malignant neoplasm of brain deaths, x10

−0,5 101 (f) Malignant neoplasm 0,2 people per 100 000 Malignant brain tumor,

Infectious diseases mortality rate, per 100 000 of brain

300 nT/year Geomagnetic ﬁ eld variation (Y-component), (g) Brain lymphoma −50 2 0,5 −0,6 (h) Infectious mortality rate incidences,person-years per 100 000 Brain Lymphoma Fractional change in breast canser mortality rate (US&UK) Fractional 100 1 900 1 920 1 940 1 960 1 980 2 000 2 020 Year

Figure 8: Time evolution (a) the variations of magnetic ﬂux at the bottom (tachocline zone) of the Sun convective zone (see Fig. 7f in [33]), (b) fractional change in female breast cancer mortality for birth cohort in US (see Fig. 3b in [34]), (c) fractional change in female 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 the westward drift of magnetic features, (e) Malignant brain tumor (brain stem) [36], (f) the number of deaths from ICD9 item n◦191 Malignant 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.

1.6 300 tive eﬀect on germ cells (according to [34]) from the 1.4

1.2 100 magnetobiological eﬀect induced by such electromag-

atom/g 1

4 -100 netic radiation as ”pearls”, since: 0.8 -300 0.6 -500 Be, promille a) electromagnetic radiation of the ”pearls” type is 0.4 10 Be, x10 10 0.2 -700 generated as a result of the protons (a dominant 1600 1700 1800 1900 2000 component of the cosmic rays) passage through the Alfvénmaser resonator, which is a magneto- Figure 9: Long-term cosmic rays reconstruction (from [45]). Cal- spheric magnetic flux tube resting upon the parts 10 culated (grey curve) and actual annual Be content in Greenland of ionosphere in the conjugate hemispheres of the ice (dotted curve). Open circles represent the 8-year data from Antarctica [44]. Red line represents the 33-year moving average Earth; of the grey curve [45]. b) the intensity variations of electromagnetic radiation of the ”pearls” type – because of their origin of a ”shadow” of galactic cosmic rays on the Earth – not only is correlated with the galactic cosmic playing the role of a proxy for the solar magnetic vari- rays variations, but also display a similar latitude ability. Therefore the variations of the solar magnetic dependence; field and galactic cosmic rays (or 10Be-proxy) must in- versely coincide which visually demonstrates the ex- c) magnetic field of the ”pearls” can freely penetrate perimentally justified result of the 1-year lag between the human body just like any other magnetic field, 10Be and sunspot originally detected by Beer et al. because the human body tissues almost do not de- [42]. After all, one could not expect anything else be- crease their intensity; indeed, the harmonic ampli- cause the galactic cosmic rays variations are caused by tude of the field with frequency ω in a oscillatory the solar magnetic field variations and not vice versa. circuit on the depth h inside the body is decreased Turning back to a direct physical cause of the cancer fs times mortality birth cohorts, it should be noted that it is practically impossible to separate the possible radia- fs(ω, h, σ, µ) = exp(−h/δ), (42) V.D. Rusov et al. ”Pearls” and Human Brain Biorhythm 11 where the path till absorption δ depends, according to [31], malignant brain tumor [36], brain lymphomas [37] [46], on the permeability µ (∼ 1) and conductivity σ, and infectious diseases (incl. Tuberculosis) [32]. and is defined as follows: δ = c(2πµωσ)−1/2. Since for The analysis of the known correlation between the 6 −1 3 ω < 10 s we have δ > 10 cm, for h 6 10 cm from galactic cosmic rays variations and cancer mortality (42) we obtain the value fs ∼ 1. birth cohorts observed for population cohorts in five Taking into account the stated properties and the countries on the three continents [34] let us suggest a known fact (e.g. [47, 48]) that the magnetic field may hypothesis of a cooperative action of the cosmic rays be a kind of an agent that amplifies the original cause and electromagnetic radiation of the ”pearls” type on (chemical impact or exposure to ionizing radiation) of the germ cells of the parents which is responsible for the carcinogenesis, we may assume that the magne- the so-called cross-generational foetal effect [34] with tobiological effect induced by the electromagnetic ra- a lag of ∼6-10 years. diation of the ”pearls” type amplifies the cosmic rays In conclusion, we have obtained results clearly show- radiative effect in the germ cells of the parents [34]. ing the possible impact of electromagnetic resonant ra- As one can easily see, the level of inverse correlation diations generated in ionospheric Alfvénmaser onto between the solar magnetic field variations (or direct stability of human brain biorhythms, such as delta- correlation between the frequency of the ”pearls” ap- rhythms and, partially, theta-rhythms. pearance) and cancer mortality rate of birth cohorts is high enough. 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