Dutt, S K

Sengupta, M M

English

IACS Institutional Repository

ON THE EVALUATION OF THE PARAMETER o-„ IN CHAPMAN’S FORMULA FOR DETERMINING THE IONIC DENSITY OF THE E LAYERBy M. M. SENGUPTA' and S. K, DUTTiRcCi'ivcJ (01 puhiii'iiiion jV otv 2^ ),ABSTRACT. Tn niir pn vious paper it has ))eeii inenlioueil that the disen pain'v :>f Ihe the iretical values of ionie fmm (^xperiiivntal ones fur K layer is due mahily to theas.smnptioii of taking const uit during day aiifl night In Hie pri'sent paper llieflulhors give tlip values of wln\h seem lo give Hie lies! agreement possible111 a previous i)ai>er (SeiiKupla ami Dutt, i ‘Ml) shown iiy lliv authors that ill the early ]>art of the nielli of winter niontlis of it>|o-.ii ladio waies of frequency .Sio ke/s Irausniilled from the Calcutta .Station (Lat. 22°34'N, lyonn. SS°55'H) reached Patna (I/at. ’ 5'^3u'N, L,ouk. 5^*^  15 'E) after reflection from the K layer while in the same period of night of summer months of 1C141 those waves penetrated the t'layei. It was also pointed out that our results were in agreement with those olitaiiicd at Watlieroo (Eat. 30*^  icj'S, Long. 1 15 °  53'E) whicli lias almost the same latitude as Patna but in the ojiposite hcnii.s]>hcre. This type of result could not he predicted from Cliapnian's ^1931) formula with a constant value of the parameter (r„ in the foimnia thmnghout day and night and for ail seasons. In the present woik an aUciiipt has been made to find siiitahle day-time and night lime values of <r„ for summer and winter months,Curves showing the variation of ion density with time (v, f) for June and Deceailier of Watheroo, are given in Figs, i and 2. Tables I and II give the values of the critical frequencies (/,) for tl layer at Watheroo observed by Parkinson and Prior (19391 1941) by the modern automatic multifrequency equipment for June of years 1938 to 1941 and for December of yeais 193S to 1940 respectively. Square values of the critical frequencies are cal­culated and finally the squares reduced lo fractions liy a suitable choice of a factor such that the midday value (obtained from the graph of hours and squares of critical frequency) corresponded to the theoretical value of i' wherev=  n/«e; n = ion-deii.sity at any time.>i„=the maximum steady value of « if the rate of production of ions were to remain constairt at its maxiimrnr jiossible value.All the critical frequencies /, in Mc/s arc for the E layer at Watheroo (lat. 30“  19'S, Long, 53'ii).* Pe)low i>f the IiiOiaii Physicnl Society.1M. M. Scngupla and S. K . DuttT able 1(Wiiitc))12n li inorm time Hours1213Mjj6nJO2n 2 1ooOJu203o/\050607vH0910 uJiim\ 193SiJune, 1039 liim*, 1940 Juiu% igii3-43 i o 7733 36 j 0.743i o,6(i3j o 6. >73 25 3 042 OsO 475 f) 27!“)I/>,S2- 57 2 933 -  21 3-34o 179.433■5^ 4(76■732351 344 337  3. "5 2/n 1 qi1 1 71.00'94Ml■73,bij07, 6(».08■79■f^51.742 S^53.023273.4 >O 773 o 742 o 713u 3S4O 427n 2 2Q n.oSf,M rj03‘\S5.-‘41033o-;.S031028027o2g•039.045.190.41 )8■ 5:'2 .672 .7303 37 3 30 3 07 2 SO 2 4" 1 8,sn 773o 741 o 041 o-5^ 7 o 4153^ 04 3 03 2 0^  2 74 2 33J O3Alean* »'o 773 o. 768 “ 733n OiS -* 1-10,78 0 041 111 1 0,0431.61 .176 i 1 52 i 0.1CJ3 1 .184'2 50 ■ 425 i 2 28 ! 4,t5 ! .423'2.90 •572 : 2 57 ; -55^ ■ 5t5s3*^ 1 .658 1 2 Qn 1 7".1 .6773-25 7^9 i 3 on 1 7S3 ■734• ITonrly critical freijneiicic s foi tlic vvliulc are available for June, 11)39 and Dcceni-ber, T93P011IVPipf Chapman’s llicory (1031)01 ionization of Uie np])er atmosphere has been apjilicd to construct curves for Watheroo showing the variation of ionic density witli time (v, (/>). (Tlie notation is according to Chapman’s paper). In actual construction the simple aiJproximate method of Millington (1932) together with his envelope coriLClion (1935) has been made use of for solving the fundamental dilTerential equation and obtaining the upper limit of theo­retical V values. Attempts were made to find the best fit with the experimental values by taking diffcient constant values for both day and niglit of parameter fT„ such as o.oT, 0.02, 0.03, etc. and the results for December and June are shown in Figs, i and 2, Ileie the aveiage declination of the sun for the resj^eclive months has *been considered and for greater accuracy points weri.- obtained at close intervals by making 02” </>i =  o.i for a few hours around noon and 03“ >^1 =  0.05 for the hours near sunset and sunrise* These results indicate that by taking constant for day and night there is no good fit. It may be noted that for a few hours round about noon, curves drawn with difTerent values of practically overlaj). The elleet of alteration in the value of is most pronounced dining ail hour or so before sunset. The 3'idue of trg corresponding to the best agreement between the theoreticalChapman"s Formula of E Layer'r\BKK II>Suiiinu^r)1 ::o 1C i Dccnnhcr . ‘938 1 h'i L inBer . >939 1 >C'U-mlu J , T94011nienn 1time 1i Me:ni 1-Hour : /, r /, i f,1 ] i r i1 11! O.C)i/} j 3 / ‘1 ; n.999 ;~ ■ 13 59 0 yt;6! 3 '■ 97 i 37-1 oy9 ; 3*94 0.974 ‘9793 ^^.5 I 904 3 .59 ' y ) 8 I 3 58 ■<M3 .92213 3 80 I 8yo 3 >^1 1 •877 ; 3 45 ‘875 .881iB I .5 50 7.55 3 i ■757 : 3 21 757 ■75f>J 7 I 3 J o 2. y» - • 1 1 2 8^s 5<)7,yj6uS - '14 ; .397 ;1-■ -^ 3 ! 35-1 1 2 22 .36^ ,361>31 ! 1 3'^  1 137 t 4 '^ 1.54 .T4I■75 j 1IJ 63 1 02472 2 ; 58 ( i2Jo23 53 ; <>>73('O15-1 i .ni79 1MJ 53 i 0)73 102 , i .0191 ;<-'3 57 01D7.60 1 U- 2 i 0 1 0 030 0.0261 ,49 i •>.U ! 1 44 M7 J 43 n 150 ■ J4306 ! 45 ! 37<’i ’ '! 2 1 ■ 373 ! 2.) 9 ■353 3<’^ 5'^7 1 3-' .577 566 ' 2. (^>9 ■ 532 •6.S«08 3 -17 ' ! 3'20 1 .729 .716 •739oy 1 79 88 s 3.49 .852 34-1 860 .866JO 3 95 ■ .1)82 3-9'<> <J->3 3.55 ■ 927 •9.1711 4 .0 1  : . 9 9  > 3 7<' !11075 3 ^71i■ ‘39 J ,9 8 6niitl uNpci inieiital curves diiiin>  ^ this period, was, Iherefore, taken as the value !.’ ivinM a gootl fit. The value ofer ,^ =  o.oi no doubt agrees closely vvilh tJie Miimner Jiionth of Deeeiiil^ei of Watlieroo mid 0.03 for winter iiiontli of June for day-time only ; h it during iiighl-tinie the agreement lads.Now, according to the theory there should be continuous decay of ionic density during the night. The j)roper values of therefore, for the night were obtained directly from the experimental observalion.s of continuous decay of the ionic density during night. It may be noted, however, that for the evaluation of the above, ob.^ervations were confined to early part of night only to avoid complications due to replenishing of the ionization which has been observed by Mitra (1938) and by Best, Farmer and Ratclifle (1938) in tlx- later part of night about 4 hours before sunrise. The values of night­time (Tq that were obtained directly are given in Table 111 and are found to be diflercnt for different seasons. They are also found to differ from day-time values for iJecember and frQ =  o,o3 giving the best fit.T abi.u IIIvSiimmer cr^December, 1938 ... 0.029January, 1939 ... 0,023Winter June, 1939 July, 19390,0590.064M. M. Sengupta and S. K . t)uU1 2 I h 24Fic;. 1rh reinl)t‘r Curve.sf-' nx|XTiiiR‘nlal rnrvc' (im an fnr vcars 1938-40 □  .Vuints of llieorclical rurvt  ^ rrp^o.o  ^A...rnillts nf theoretical rurve with erg —n.nlF i Ct. 2 June Curves(0,..Experimental curves liman for years 1938^4j; \* ,..roint8 of theoretical curve with otq^ . oj □  ..Points of theoretical curve with trQ= 02 A...Points of theoretical curve with <ros=.oiChapman's Fotmula oj E Layer 517 1 iS 1 ijIlnursImCi . 3A , A . ..Tlu'iUTliral cm vi-uirvcJunr, .vj »'ui‘VL' (lull line i <rQ- oo,^ flnv tjiiic)l)L’Cciiibcr, 3iS cm vf ihrokcn liiici (f(j 0.01 (das-lime) iTo^0.029 Iniglit-tiiiic)I'o obtain the best lit, therefore, it is necessary to take different values of (Tq for seasons as well as for day and night. The theoretical ciuves of h i^g. 3 are drawn with <^  ^=  0,01 (day-time), —0,029 biight-tinie) for December (summer) and with ctq=:o.u3 (day-tirne), 0.05(9 (night-time) for June (winter) in which the experimental data arc also plolted fur compari^ son ; the agreement comes out to be very close both for day and night and for seasons also.Summer and winter (i\ 0) curves derived from Chapman s formula with a constant values of for day aud night throughout tlie year, will not intersect each other as tlie rate of ionization at any hour in summer is greater than that in wdiiter for the same hour. Hut with different values of the theoretical curves (Fig. 3) do intersect and agree with the experimental observations. The net result of different values of is that the night-time ionic density of E  layer for winter is larger than that for sunimer, though the noon value for the latter season is mucli higher than that for the winter.Tliat <T(, has difTerenl values for and day has been observu-d byBest, I'armcT and RatclifTe (/or. til.). They found Hial for bolli summer and winter the uighl-liine value of ir  ^ is o.ogS corresponding to recombination co-efTicient « =  4 X lo"* and day-time value of Tq a little gieater tlian 0.032 corresiiomling to « = i .a x io ~ " ,  That it is necessary to assume a greater rate of recombination during the day than during the night, is confirmed by some curves calculated by Wilkes (iy39j from observations made at Washing­ton (Lat. 38"’ 50' N, lyong. 77" on' W) on 31st August, 1932, wlien an eclipse of the sun look place, <5 by Kirby, (iillilaiid and Judsou (1936). lie  points out that the day-time curves on eclipse day with cr„ =  o, a very large or ctq =  0.032, fit in with the experimental curves better than the one for (T,, =  0.098. Hulburt (1939) concludes that during day-time the avaiiabfe data favour a-,, =  0.011) («= 2  x io “ ") but do not iireclude an even lower value of a higher rale of recombination.Another point to be noted is that the .summer night time value of cr for Watiieroo is found to be apjiroxiinately 3 times tlie day-time value of while winter night-time value is twice that during day-time. The night-' time and day-time values of as observed by Best, h'armer and Ratclifle aie in the ratio of 3 : 1 .From the above it is clear that the values of '»o obtained from the data of Watiieroo are quite probable in view of the determinations of Ilulburt, and of Best, fi'anner and RalclilTe. It has been showm by us (Sengupta and Dutt, 1944, iliat the behaviour of the iono.sjihere in the Patna-Calcutta legion fabout 2 1*-^ N latitude) has been exiieiiinentally found to be similar to that of Watiieroo, so far as the ionic densities of summer and winter are concerned ; it, therefore, seems that the most probable values of (r(, for latitudes 24° to 30'  ^ North or vSoutli, may be taken as given above.P h ysics L ahoratokv,SClIvNCll Couiioii,Paina6 M. M, Sengupia and $. K. DuffR E F E R E K C E SBe.st, Farmer and Eatcliffe, 1938, P.R.S, (.-I), 164, 96.Chapman, 1931, Proc. Phy. Soc. (Loud.), 43, 26 and 483. lUiUnut, 1939, Phy. Rev., 66, 639.Kirliy, Gilliland and Jndson, 1936, Proc. I.R.E , 24, 1027.Millington, 1932, Proc. Phy. Soc. <Lond.)H, 580.Millington, 1935, Proc. Phy. Soc, <Lond ), 47, 263.Mitra, 1938, Science and Culture, 3, 496.I’iiikinsoii and Prior, 1939,.'rn i, Mng. /t: /Knios. Elec. 44, 199. 341 4 40I; 1940, Ibid , 48, 45 & 471; 1941, ibid., 46, 79.Sengupta and Dutt, 1944, Ind. Jour. Phy,, 18, 88.Wilkes, 1939, Prof, Phy. See,, 81, 138.

On the Evaluation of the Parameter δo in Chapman’s Formula for Determining the Ionic Density of the E Layer

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On the Evaluation of the Parameter δo in Chapman’s Formula for Determining the Ionic Density of the E Layer

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