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X / / \\-> ->v v ""//"max >

Fít,Xo0,W(t - X)XE j = J0 íWX)3 3 X-0dX, (2.45.5)

X = r/u , XE = 1AU/u, Xo = ro/u ( XE and Xo are in units of average month =

(365.25/12) days = 2.628 x106 sec). Let us note that the solving of Eq. 2.45.4 on the basis of experimental data will give solution also for the inverse problem because the regression coefficient A((,Xo,0) determines the CR intensity out of the Heliosphere, regression coefficient b(r,Xo,0) characterized the effective diffusion coefficient of CR in the interplanetary space, and Xo = ro/u characterized the dimension of modulation region. These three coefficients can be determined by correlation between observed values ln(«(R,rE, t)obs ) and the values of F, calculated according to Eq. 2.45.5 for different values of Xo and 0. In Dorman et al. (1997) three values of 0 = 0; 0.5; 1 have been considered; it was shown that 0 = 1 strongly contradicts CR and SA observation data, and that 0 = 0 is the most reliable value. Therefore, we will consider here only this value.

2.45.3. Even-odd cycle effect in CR and role of drifts for NM energies

To determine Xo max, corresponding to the maximum value of the correlation coefficient for regression Eq. 2.45.4, we compare 11 months moving averages of the Climax NM (H = 3400 m, cut-off rigidity Rc = 2.99 GV) for solar cycles 19-22 and onset of cycle 23 (Dorman, 2001). For each time-lag, Xo = ro/u =1, 2, 3, ... 60 av. months, we determined the correlation between observed and expected CR intensities. The Climax NM data correspond to an effective rigidity of primary CR

of about 10-15 GV. For higher energy particles (about 30-40 GV) we used Huancayo (Rc = 12.92 GV, H = 3400 m)/Haleakala (Rc = 12.91 GV, H = 3030 m) NM data from January 1953 to August 2000. Results are summarized below in Table 2.45.1 in columns Adr =0%. It can be seen a big difference in Xo max for odd and even solar cycles.

We assume that observed long-term CR modulation is caused by two processes: the convection-diffusion mechanism (e.g. Parker, 1958, M1963; Dorman, 1959c, 1965), which is independent of the sign of the solar magnetic field, and the drift mechanism (e.g., Jokipii and Davila, 1981; Burger and Potgieter, 1999; Ferreira et al., 1999), what gave opposite effects with changing sign of solar magnetic field. For the convection-diffusion mechanism we use the model described in detail in Dorman (2001), shortly given above by Eqs. 2.45.1- 2.45.5. For drift effects we use results of Burger and Potgieter, 1999 (see also above, Section 2.37), and assume that the drift effect is proportional to the value of the tilt angle a with negative sign at A > 0 and positive sign at A < 0, and in the period of reversal we again suppose linear transition through 0 from one polarity cycle to other (see Fig. 2.37.1-2.37.4 in Section 2.37; we assume that average of curves for A > 0 and A < 0 in these figures characterized convection-diffusion modulation, and difference of these curves -double drift modulation). Data on tilt-angles for solar cycles 19 and 20 are not available. We used relation between sunspot numbers W and a to made homogeneous analysis of the period 1953-2000. Based on data for 18 years (May 1976- September 1993), we found that there are very good relation between a and W; for 11 months smoothed data a= 0.349W + 13.5° (2.45.6)

with correlation coefficient 0.955. An example for correction of observed CR intensity on the drift effects (to obtain only convection-diffusion modulation) is shown for period January 1953-November 2000 in Fig. 2.45.1. We used 11 months smoothed data of W (shown in Fig. 2.45.1) and determined the amplitude A^r of drift effects as drift modulation at W11M = 75 (average value of

W11M for 1953-1999). The reversal periods were determined as: August 1949 ± 9 months, December 1958 ± 12 months, December 1969 ± 8 months, March 1981 ± 5 months, and June 1991 ± 7 months. We determined correlation coefficients between the expected integrals F according to Eq. 2.45.5 for different values of Xo = 1, 2, 3, ... 60 av months with the observed LN(CL11M) and LN(HU/HAL 11M), as well as with corrected for the drift effects according to Adr from 0.15% up to 4%.

In Table 2.45.1 are shown results of the determination of Xo max for solar cycles 19, 20, 21, and 22 without corrections on drift effect, and with corrections owed to the drift effects in dependence of the value of Adr (from 0.5% to 4% for Climax NM and from 0.15% to 1.0% for Huancayo/Haleakala NM).

Fig. 2.45.1. An example of CR data correction on drift effects in 1953-2000 (19-22 cycles and onset of 23 cycle): LN(CL11M) - observed natural logarithm of Climax NM counting rate smoothed for 11 months, LN(CLCOR3_DR2%) - corrected on assumed Adr =2% at W11M=75. Interval between two horizontal lines corresponds 5% of CR intensity variation.

Fig. 2.45.1. An example of CR data correction on drift effects in 1953-2000 (19-22 cycles and onset of 23 cycle): LN(CL11M) - observed natural logarithm of Climax NM counting rate smoothed for 11 months, LN(CLCOR3_DR2%) - corrected on assumed Adr =2% at W11M=75. Interval between two horizontal lines corresponds 5% of CR intensity variation.

Table 2.45.1. Values of Xo max (in av. months) for observed data (Adr = 0%) and corrected on drift effects with different amplitudes .

CLIMAX NM, LN(CL11M)

cy

0%

0.5%

1%

1.5%

2%

2.5%

3%

4%

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