Laboratory calibration measurements of a piezoelectric lead zirconate titanate cosmic dust detector at low velocities

A cosmic dust monitor for use onboard a spacecraft is currently being developed using a piezoelectric lead zirconate titanate element (PZT). Its characteristics of the PZT sensor is studied by ground-based laboratory impact experiments using hypervelocity particles supplied by a Van de Graaff accelerator. The output signals obtained from the sensor just after the impact appeared to have a waveform that was explicitly related to the particle’s impact velocity. For velocities less than ∼6 km/s, the signal showed an oscillation pattern and the amplitude was proportional to the momentum of the impacting particle. For higher velocities, the signal gradually changed to a single waveform. The rise time of this single waveform was proportional to the particle’s velocity for velocities above ∼6 km/s. The present paper reports on results for the low velocity case and especially discusses the effect of an outer coating of the sensor with a paint, which is used to reduce heating by solar radiation.     

Multimodal characteristics of a piezoelectric lead zirconate titanate element impacted with iron particles having velocities above 20 km/s

The responses of a piezoelectric lead zirconate titanate (PZT) element to hypervelocity collisions were experimentally studied. In this study, the particles of masses ranging from 0.3 to 10 fg were made to collide with PZT at velocities between 20 and 96 km/s. The amplitude and the corresponding rise time of the single-pulse output signals that were produced in the piezoelectric PZT element were measured to determine the possible collision states. The results revealed an apparently multimodal output; three classes were assumed to be involved in the pulse formation mechanism. The amplitude and rise time were sensitive to the collision velocity. The multimodal behavior implied that the PZT-based cosmic dust detectors should be calibrated according to the class they belong to.     

Detection of meteors and sub-relativistic dust grains by the fluorescence detectors of ultra high energy cosmic rays

Fluorescence detectors of ultra high energy cosmic rays (UHECR) allow to record not only the extensive air showers, initiated by the UHECR particles, but also to detect light, produced by meteors and by the fast dust grains. It is shown that the fluorescence detector operated at the mountain site can register signals from meteors with kinetic energy threshold of about 25 J (meteor mass ∼ 5 × 10⁻⁶ g, velocity ∼ 3 × 10⁶ cm/s). The same detector might be used for recording of the dust grains of smaller mass (of about 10⁻¹⁰ g) but with velocity 10⁹ cm/s, close to the light velocity (sub-relativistic dust grains). The light signal from a sub-relativistic dust grain is expected in much shorter time scale (∼0.001 s), in comparison with the meteor signal (∼0.1–1 s), and much longer than duration of the UHECR signals (tens of μs). The fluorescence detector capable to register various phenomena: from meteors to UHECR – should have a variable pixel and selecting system integration time. A study of the new phenomenon of sub-relativistic grains will help to understand the mechanism of particle and dust grain acceleration in astrophysical objects (in SN explosions, for example).     

On the production of highest energy solar protons at 20 January 2005

On January 20, 2005, 7:02–7:05 UT the Aragats Multidirectional Muon Monitor (AMMM) located at 3200 m a.s.l. registered enhancement of the high energy secondary muon flux (threshold ∼5 GeV). The enhancement, lasting for 3 min, has statistical significance of ∼4σ and is related to the X7.1 flare seen by the GOES, and very fast (>2500 km/s) CME seen by SOHO, and the Ground Level Enhancements (GLE) #69 detected by the world-wide network of neutron monitors and muon detectors. The energetic and temporal characteristics of the muon signal from the AMMM are compared with the characteristics of other monitors located at the Aragats Space-Environmental Center (ASEC) and with other neutron and muon detectors. Since secondary muons with energies >5 GeV are corresponding to solar proton primaries with energies 20–30 GeV we conclude that in the episode of the particle acceleration at 7:02–7:05 UT 20 January 2005 solar protons were accelerated up to energies in excess of 20 GeV.     

Creating an artificial Geminid meteor shower: Correlation between ejecta velocity and observability

One of the interesting arguments for a space impact mission to asteroid 3200 Phaethon is to create an artificial Geminid meteor shower. In this work we investigate the artificial shower’s dates of observability and dependence on ejecta velocity using dust trail theory. We find that when the dust ejecta velocities are 200 m/s the artificial meteor showers start to be visible in 2204 and continue for about 30 years. If the dust ejecta velocity is 20 m/s they only last 10 years from 2215 to 2225. Thus, the onset of artificial shower activity begins sooner and lasts longer with higher ejecta velocities. To produce an artificial meteor shower with 3200 Phaethon as the parent will require higher impact energy than the Deep Impact spacecraft delivered to 9P/Tempel 1.     

The 16-day waves in the mesosphere and lower thermosphere over Wuhan (30.6°N, 114.5°E) and Adelaide (35°S, 138°E)

Winds from a meteor radar at Wuhan (30.6°N, 114.5°E) and a MF radar at Adelaide (35°S, 138°E) are used to study the 16-day waves in the mesosphere and lower thermosphere (MLT). The height range is 78–98 km at Wuhan and 70–98 km at Adelaide. By comparison, it is found that the zonal components at both sites are generally larger than the meridional ones, and eastward motion of the zonal background winds is favorable for the 16-day waves penetration to the MLT region. The zonal maximum amplitude appears in the autumn (September–October) around 86–98 km at Wuhan and in the winter months and early spring (July–October) around 72–82 km at Adelaide. Differences are found in wave amplitudes and time of appearance between the two years of 2002 and 2003. In 2003, the intensity of the wave amplitudes is relatively smaller than that for 2002 at both sites. The summer 16-day waves are comparatively weaker at Adelaide in both years, but stronger in 2002 at Wuhan near the mesopause and the lower thermosphere (86–98 km). The strong summer waves at Wuhan may come from the winter southern hemisphere.     

Characterization of the semi-annual-oscillation in mesospheric temperatures at low-latitudes

Novel measurements of the seasonal variability in mesospheric temperature at low-latitudes have been obtained from Maui, Hawaii (20.8°N, 156.2°W) during a 25-month period from October 2001 to January 2004. Independent observations of the OH (6, 2) Meinel band (peak height ∼87 km) and the O₂ (0–1) atmospheric band emission (∼94 km) were made using the CEDAR Mesospheric Temperature Mapper. The data revealed a coherent oscillation in emission intensity and rotational temperature with a well-defined periodicity of 181 ± 7 days. The amplitude of this oscillation was determined to be ∼5–6 K in temperature and ∼8–9% in intensity for both the OH and O₂ data sets. In addition, a strong asymmetry in the shape of the oscillation was also observed with the spring maximum significantly larger than the fall peak. These data provide new evidence in support of a semi-annual-oscillation in mesospheric temperature (and airglow emission intensities) and help quantify its seasonal characteristics.     

Satellite monitoring of anomalous effects in the ionosphere probably related to strong earthquakes

The paper presents simultaneously a satellite monitoring of plasma density disturbances and quasi-static electric fields on the one hand, and a ground earthquake monitoring, on the other. The INTERCOSMOS-BULGARIA-1300 satellite was launched on 7th August 1981. It had a perigee of 825 km, an apogee of 906 km and orbit inclination of 81.2°. For satellite’s orbits over sources of earthquakes M ⩾ 5.5 (seismic data of the World Data Center – Denver, Colorado), in the time period 12.08.1981–30.12.1981, some ionospheric effects are investigated. These effects can be considered eventually as possible earthquake precursors. The paper discusses specific anomalous effects observed in the ionosphere, which cannot be explained by factors of solar-magnetospheric origin. They could be associated with the earthquake growing processes in the lithosphere and troposphere zones above the source. In conclusion the results of ionosphere anomalous effects monitoring are proposed.     

USV test flight by stratospheric balloon: Preliminary mission analysis

The Unmanned Space Vehicle test flights will use a 7 m 1300 kg aircraft. The first three launches will take place at the Italian Space Agency ASI base in Trapani–Milo, Sicily, through a stratospheric balloon that will drop the aircraft at a predefined height. After free fall acceleration to transonic velocities, the parachute deployment will allow a safe splash down in the central Mediterranean Sea. The goal of this article is to show the preliminary analysis results for the first USV flight.We carried out a statistical study for the year 2000–2003, evaluating the typical summer and winter launch windows of the Trapani–Milo base.First, in the center Mediterranean, we define safe recovery areas. They cannot be reached during the balloon ascending phase so, after a sufficiently long floating part able to catch the open sea, the balloon will go down to the release height (24 km). The simulation foresees a 400,000 m³ balloon and 3 valves for the altitude transfer.A safe splash down must occur far enough from the nearest coast: the minimum distance is considered around 25 km. The vehicle should be released at a distance, from the nearest coast, greater than this minimum amount plus the USV model maximum horizontal translation, during its own trajectory from balloon separation to splash down. In this way we define safe release areas for some possible translations.Winter stratospheric winds are less stable. The winter average flight duration is 7 h and it is probably too long for the diurnal recovery requirement and its scheduled procedures.Comparing past stratospheric balloons flights and trajectories computed using measured meteorological data (analysis), with their predictions made using forecast models and soundings, we obtain the standard deviation of the trajectory forecast uncertainty at the balloon–aircraft separation. Two cases are taken into account: predictions made 24 and 6 h before the launch.Assuming a Gaussian latitudinal uncertainty distribution for the prediction 6 h before the launch, we are able to identify the forecast trajectories that have a probability greater than 97% to reach the safe release areas.Simulating the summer windows trajectories for the years from 2000 to 2003 and for the favorable ground wind days, we obtain the number of trajectories with the desired forecast probabilities.     

Analysis of electromagnetic and electrostatic effects of particle impacts on spacecraft

Particle impacts on spacecraft can cause considerable damage, even leading to complete failure. A theory for the resulting vehicle potential changes and the electromagnetic radiation from impact-induced plasma has been published by Close et al. (2010). Here we compare this theory to impacts registered by the Radio and Plasma Wave Science instrumentation on the Cassini spacecraft. We study both low-velocity (16 km/s) large particles (2.6 μm radius) detected in Saturn’s rings and high-velocity (450 km/s) small particles (1 nm radius) in the solar wind. The agreement with the theory is quite good. We also apply these results to earth orbit and conclude that both Electrostatic Discharge and Electromagnetic Pulse radiation are likely and could lead to spacecraft failure.     

Development of a 2.8 μm film for scientific balloons

Development of a balloon to fly at higher altitudes is one of the most attractive challenges in scientific balloon technologies. After reaching the highest record setting balloon altitude of 53.0 km using the 3.4 μm film in 2002, we tried to make a thinner balloon film. In 2003, we developed a forming die and an air-ring and succeeded in forming a film with a thickness of 3.0 μm and a width of 220 cm. Using this film, we manufactured a balloon with a volume of 5000 m³ and succeeded in flying the balloon up to an altitude of 46.0 km. We then searched for a good combination of resins to make a thinner and wider film and obtained films with widths of 280 cm, and a thickness of 3.0 μm at first, and then 2.8 μm. In 2004, we performed balloon experiments making a 30,000 m³ balloon with the 3.0 μm film and a 5000 m³ balloon with the 2.8 μm film. Both balloons were well manufactured and reached the highest altitudes of 50.7 and 42.6 km, respectively.     

Hard X-ray footpoint motions in solar flares: Comparing magnetic reconnection models with observations

Hard X-ray observations from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) of the October 29, 2003 GOES X10 two-ribbon flare are used together with magnetic field observations from the Michelson Doppler Imager (MDI) onboard SoHO to compare footpoint motions with predictions from magnetic reconnection models. The temporal variations of the velocity v of the hard X-ray footpoint motions and the photospheric magnetic field strength B in footpoints are investigated. The underlying photospheric magnetic field strength is generally higher (B ∼ 700–1200 G) in the slower moving (v ∼ 20–50 km s⁻¹) western footpoint than in the faster (v ∼ 20–100 km s⁻¹) moving eastern source (∼100–600 G). Furthermore, a rough temporal correlation between the HXR flux and the product vB² is observed.     

Measurement of turbulent kinetic energy dissipation rates in the mesosphere by a 3 MHz Doppler radar

A new narrow beam Doppler radar operating at 3.17 MHz has been installed close to the Andøya Rocket Range in Andenes, Norway in summer 2002 in order to improve the ground based capabilities for measurements of turbulence in the mesosphere. The main feature of the radar is a Mills Cross transmitting/receiving antenna consisting of 29 crossed half-wave dipoles. In combination with the modular transceiver system this provides high flexibility in beam forming and pointing. In general, vertical and oblique beams with a minimum one way half-power full-beam width (HPFW) of 6.6° are used. The observations are usually performed with a height resolution of 1 km and with off-zenith beams at 7.3° directed towards NW, NE, SE, and SW. Turbulence intensities have been estimated from the width of the observed signal spectra using an computationally intensive correction method which requires precise knowledge of the antenna radiation pattern. The program uses real-time measurements of the wind field in all determinations. Turbulent kinetic energy dissipation rates based on radar observations are presented and compared with corresponding climatological summer and winter profiles from rocket measurements, as well as with single profiles from model runs for selected periods from September 2003 to Summer 2004. The mean turbulent kinetic energy dissipation rates based on these radar measurements are about 5 mW/kg at 60 km altitude and about 20 mW/kg at 80 km, in reasonable agreement with mean turbulence intensities obtained from previous rocket soundings at Andenes.     

F2 layer characteristics and electrojet strength over an equatorial station

The data presented in this work describes the diurnal and seasonal variation in hmF2, NmF2, and the electrojet current strength over an African equatorial station during a period of low solar activity. The F2 region horizontal magnetic element H revealed that the Solar quiet Sq(H) daily variation rises from early morning period to maximum around local noon and falls to lower values towards evening. The F2 ionospheric current responsible for the magnetic field variations is inferred to build up at the early morning hours, attaining maximum strength around 1200 LT. The Sq variation across the entire months was higher during the daytime than nighttime. This is ascribed to the variability of the ionospheric parameters like conductivity and winds structure in this region. Seasonal daytime electrojet (EEJ) current strength for June solstice, March and September equinoxes, respectively had peak values ranging within 27–35 nT (at 1400 LT) , 30–40 nT (at 1200 LT) and 35–45 nT (at 1500 LT). The different peak periods of the EEJ strength were attributed to the combined effects of the peak electron density and electric field. Lastly, the EEJ strength was observed to be higher during the equinoxes than the solstice period.     

Comparison of vertical E × B drift velocities and ground-based magnetometer observations of DELTA H in the low latitude under geomagnetically disturbed conditions

In the present work, we analyzed the daytime vertical E × B drift velocities obtained from Jicamarca Unattended Long-term Ionosphere Atmosphere (JULIA) radar and ΔH component of geomagnetic field measured as the difference between the magnitudes of the horizontal (H) components between two magnetometers deployed at two different locations Jicamarca, and Piura in Peru for 22 geomagnetically disturbed events in which either SC has occurred or Dst_max < ?50 nT during the period 2006–2011. The ΔH component of geomagnetic field is measured as the differences in the magnitudes of horizontal H component between magnetometer placed directly on the magnetic equator and one displaced 6–9° away. It will provide a direct measure of the daytime electrojet current, due to the eastward electric field. This will in turn gives the magnitude of vertical E × B drift velocity in the F region. A positive correlation exists between peak values of daytime vertical E × B drift velocity and peak value of ΔH for the three consecutive days of the events. It was observed that 45% of the events have daytime vertical E × B drift velocity peak in the magnitude range 10–20 m/s and 20–30 m/s and 20% have peak ΔH in the magnitude range 50–60 nT and 80–90 nT. It was observed that the time of occurrence of the peak value of both the vertical E × B drift velocity and the ΔH have a maximum (40%) probability in the same time range 11:00–13:00 LT. We also investigated the correlation between E × B drift velocity and D_st index and the correlation between delta H and D_st index. A strong positive correlation is found between E × B drift and D_st index as well as between delta H and D_st Index. Three different techniques of data analysis – linear, polynomial (order 2), and polynomial (order 3) regression analysis were considered. The regression parameters in all the three cases were calculated using the Least Square Method (LSM), using the daytime vertical E × B drift velocity and ΔH. A formula was developed which indicates the relationship between daytime vertical E × B drift velocity and ΔH, for the disturbed periods. The E × B drift velocity was then evaluated using the formulae thus found for the three regression analysis and validated for the ‘disturbed periods’ of 3 selected events. The E × B drift velocities estimated by the three regression analysis have a fairly good agreement with JULIA radar observed values under different seasons and solar activity conditions. Root Mean Square (RMS) errors calculated for each case suggest that polynomial (order 3) regression analysis provides a better agreement with the observations from among the three.     

Spectral filter for signal identification in the kHz SLR measurements of the fast spinning satellite Ajisai

The high repetition rate satellite laser ranging (SLR) measurements to the fast spinning satellites contain a frequency signal caused by the rotational motion of the corner cube reflector (CCR) array. The spectral filter, developed here, is based on the Lomb algorithm, and is tested with the simulated and the observed high repetition rate SLR data of the geodetic satellite Ajisai (spin period ∼2 s). The filter allows for the noise elimination from the SLR data, and for identification of the returns from the single CCRs of the array – even for the low return rates. Applying the spectral filter to the simulated SLR data increases the S/N ratio by a factor 40–45% for all return rates. Filtering out the noise from the observed data strengthens the frequency signal by factor of ∼25 for the low return rates, which significantly helps to determine the spin phase of the satellite. The spectral filter is applied to the Graz SLR data and the spin rates of Ajisai are determined by two different methods: the frequency analysis and the phase determination of the spinning retroreflector array.The analysis of more than 8 years of the Graz SLR measurements indicates an exponential spin rate trend: f = 0.67034 exp(−0.0148542 Y) [Hz], RMS = 0.085 mHz, where Y is the year since launch. The highly accurate spin rate information demonstrates periodic changes related to the precession of the orbital plane of Ajisai, as it determines the amount of energy received by the satellite from the Sun. The rate of deceleration of Ajisai is not constant: the half life period of the satellite’s spin oscillates around 46.7 years with an amplitude of about 5 years.     

Global MGS TES data and Mars-GRAM validation

Mars Global Reference Atmospheric Model (Mars-GRAM 2001) is an engineering-level Mars atmosphere model widely used for many Mars mission applications. From 0 to 80 km, it is based on NASA Ames Mars General Circulation Model (MGCM), while above 80 km it is based on University of Michigan Mars Thermospheric General Circulation Model. Mars-GRAM 2001 and MGCM use surface topography from Mars Global Surveyor Mars Orbiter Laser Altimeter (MOLA). Validation studies are described comparing Mars-GRAM with a global summary data set of Mars Global Surveyor Thermal Emission Spectrometer (TES) data. TES averages and standard deviations were assembled from binned TES data which covered surface to ∼40 km, over more than a full Mars year (February 1999–June 2001, just before start of a Mars global dust storm). TES data were binned in 10° × 10° latitude–longitude bins (36 longitude bins, centered at 5°–355°, by 18 latitude bins, centered at −85° to +85°), and 12 seasonal bins (based on 30° increments of L_s angle). Bin averages and standard deviations were assembled at 23 data levels (temperature at 21 pressure levels, plus surface temperature and surface pressure). Two time-of-day bins were used: local time near 2 or 14 h. Two dust optical depth bins were used: infrared optical depth, either less than or greater than 0.25 (which corresponds to visible optical depth less than or greater than about 0.5). For interests in aerocapture and precision entry and landing, comparisons focused on atmospheric density. TES densities versus height were computed from TES temperature versus pressure, using assumptions of perfect gas law and hydrostatics. Mars-GRAM validation studies used density ratio (TES/Mars-GRAM) evaluated at data bin center points in space and time. Observed average TES/Mars-GRAM density ratios were generally 1 ± 0.05, except at high altitudes (15–30 km, depending on season) and high latitudes (>45°N), or at most altitudes in the southern hemisphere at L_s ∼ 90° and 180°. Compared to TES averages for a given latitude and season, TES data had average density standard deviation about the mean of ∼2.5% for all data, or ∼1–4%, depending on time of day and dust optical depth. Average standard deviation of TES/Mars-GRAM density ratio was 8.9% for local time 2 h and 7.1% for local time 14 h. Thus standard deviation of observed TES/Mars-GRAM density ratio, evaluated at matching positions and times, is about three times the standard deviation of TES data about the TES mean value at a given position and season.     

The high altitude student platform (HASP) for student-built payloads

An outstanding issue with aerospace workforce development is what should be done at the university level to attract and prepare undergraduates for an aerospace career. One approach adopted by many institutions is to lead students through the design and development of small payloads (less than about 500 grams) that can be carried up to high altitude (around 30 km) by a latex sounding balloon. This approach has been very successful in helping students to integrate their content knowledge with practical skills and to understand the end-to-end process of aerospace project development. Sounding balloons, however, are usually constrained in flight duration (∼30 min above 24 km) and payload weight, limiting the kinds investigations that are possible. Student built picosatellites, such as CubeSats, can be placed in low Earth orbit removing the flight duration constraint, but the delays between satellite development and launch can be years. Here, we present the inexpensive high altitude student platform (HASP) that is designed to carry at least eight student payloads at a time to an altitude of about 36 km with flight durations of 15–20 h using a small zero-pressure polyethylene film balloon. This platform provides a flight capability greater than sounding balloons and can be used to flight-test compact satellites, prototypes and other small payloads designed and built by students. The HASP includes a standard mechanical, power and communication interface for the student payload to simplify integration and allows the payloads to be fully exercised. HASP is lightweight, has simple mission requirements providing flexibility in the launch schedule, will provide a flight test opportunity at the end of each academic year.     

XMM-Newton observations of the Mouse,SLX 1744–299 and SLX 1744–300

We observed the radio and X-ray source G359.23–0.82, also known as “the Mouse”, with XMM-Newton. The X-ray image of this object shows a point-like source at the Mouse’s “head”, accompanied by a “tail” that extends for about 40″ westward. The morphology is consistent with that observed recently with Chandra [Gaensler, B.M., van der Swaluw, E., Camilo, F., et al. The Mouse that soared: high resolution X-ray imaging of the pulsar-powered bow shock G359.23–0.82, ApJ 616, 383–402, 2004]. The spectrum of the head can be described by a power-law model with a photon index Γ ≃ 1.9. These results confirm that the Mouse is a bow-shock pulsar wind nebula (PWN) powered by PSR J1747–2958. We found that the hydrogen column density toward the Mouse, N_H = (2.60 ± 0.09) × 10²² cm⁻², is 20%–40% lower than those toward two serendipitously detected X-ray bursters, SLX 1744–299 and SLX 1744–300. At a plausible distance of 5 kpc, the X-ray luminosity of the Mouse, L(0.5–10 keV) = 3.7 × 10³⁴ erg s⁻¹, is 1.5% of the pulsar’s spin-down luminosity. We detected a Type I X-ray burst from SLX 1744–300 and found a possible decrease of N_H and persistent luminosity for this source, in comparison with those observed with ROSAT in 1992.     

The role of drift and convection–diffusion mechanisms in small energy global cosmic ray modulation: Application to the hysteresis phenomenon of proton and alpha particle satellite data

The hysteresis effect for small energies of galactic cosmic rays is due to two effects. The first is the same as for neutron monitor energies – the delay of the interplanetary processes responsible for cosmic ray modulation with respect to the initiating solar processes, according to the effective velocity of solar wind and shock waves propagation. Then, the observed cosmic ray intensity is connected to the solar activity variations during many months before the time of cosmic ray measurement. The second is caused by the time delay of small energy cosmic ray diffusion from the boundary of modulation region to the Earth’s orbit. The model describing the connection between solar activity variation and cosmic ray convection–diffusion global modulation for neutron monitor energies is here developed by taking into account also the time-lag of the small energy particle diffusion in the Heliosphere. We use theoretical results on drifts and analytically approximate the dependences of drifts from tilt angle, and take into account the dependence from the sign of primary particles, and from the sign of polar magnetic field (A > 0 or A < 0). The obtained results are applied on proton and alpha-particle satellite data. We analyze satellite 5-min data of proton fluxes with energies >1 MeV, >2 MeV, >5 MeV, >10 MeV, >30 MeV, >50 MeV, >60 MeV, >100 MeV, and in intervals 10–30 MeV, 30–60 MeV, and 60–100 MeV during January 1986–December 1999. We exclude periods with great cosmic ray increases caused by particle acceleration in solar flare events. Then, we determine monthly averaged fluxes, as well as 5-month and 11-month smoothed data. We analyze also satellite 5-min data on alpha-particle fluxes in the energy intervals 60-160 MeV, 160–260 MeV and 330–500 MeV during January 1986–May 2000. We correct observation data for drifts and then compare with what is expected according to the convection–diffusion mechanism. We assume different dimensions of the modulation region (by the time propagation X₀ of solar wind from the Sun to the boundary of modulation region), for X₀ values from 1 to 60 average months, by one-month steps. For each value of X₀ we determine the correlation coefficient between variations of expected and observed cosmic ray intensities (the estimation of cosmic ray intensities values is given in Section 3 by Eq. (9), and the determination of correlation and regression coefficients in Section 3 by Eq. (8)). The dimension of modulation region is determined by the value of X_0 max, for which the correlation coefficient reaches the maximum value. Then the effective radial diffusion coefficient and residual modulation in small energy region can be estimated.