Laboratory studies of the charging of soft-hail during ice crystal interactions

Quart. J . R . Met . SOC. (1983), 109, pp. 609430 551.578.71 :551.594.252

Laboratory studies of the charging of soft-hail during ice crystal interactions

By E. R. JAYARATNE', C. P. R. SAUNDERS and J. HALLETT' Physics Department, U M I S T , Manchester, M 6 0 I Q D

(Received 26 January 1982, revised 4 January 1983)

SUMMARY A laboratory investigation of electric charge transfer during the impact of vapour-grown ice crystals and

supercooled water droplets upon a simulated soft-hailstone target has shown that the magnitude of the charge transferred to the riming surface when crystals separate from it is a function of temperature, crystal dimension, relative velocity, liquid water content, and impurity content of the water droplets and hence the impurity content of the riming target. The sign of the charge transfer depends on temperature, liquid water content and droplet and rime impurity content.

In the absence of crystals, no charge transfer was detected during riming. In the absence of supercooled water droplets, crystals impacting at 10m s- on an evaporating rime target produced a small negative charge on the rime of less than -0.25fC per separating crystal. When the target surface grew by vapour diffusion it gained a small positive charge during such interactions. Much larger charges and completely different charge transfer behaviour was noted during riming. The target became positively charged at high liquid water contents and temperatures above a critical value, but negatively charged at lower temperatures or with lower liquid water contents. The critical sign reversal temperature at a liquid water content of 1 g m - 3 was about -20°C. At -10°C with a liquid water content of 2gm-3, a 125pm crystal impacting at 3ms-I charged the target by + lOfC upon separation. The charge transfer increased sharply with impact speed and crystal size. Warming the positively charging rime to cause it to evaporate failed to reverse the sign of the charge transfer. Experiments with impurities showed that the sign reversal temperature increased if the droplets contained contaminants at concentrations found in cloud water.

It is suggested that there are two distinct charge transfer processes during crystal interactions with an ice target, the dominant one requiring the presence of supercooled water droplets. Careful control and knowledge of the microphysical properties of the clouds used in these experimental simulations has permitted an exami- nation of charge transfer under many of the conditions used in previous studies. The results provide an understanding of the differences and a reconciliation between some of the previously disparate findings in terms of the two distinct charge transfer regimes.

1. INTRODUCTION In his review of the electrification of thunderstorms, Latham (1981) noted the

growing quantity and quality of evidence that one of the principal electric charge transfer mechanisms within thunderstorms involves collisions between small, soft-hail pellets, supercooled water droplets and ice crystals. The evidence for this conclusion is based on radar, electric field and radiation data including that of Lhermitte and Krehbiel (1979) and Krehbiel et al. (1979, 1980) who found, in agreement with other workers, that the negative charge centres within thunderclouds are co-located with precipitation within well-defined temperature zones above the freezing level. Aircraft penetrations of clouds reported by Gaskell et al. (1978) and Christian et al. (1980) have shown that integrated volume charge densities due to electric charges on individual precipitation particles in supercooled regions can reach values of the order of 1 C km-3. This is a substantial fraction of the average space charge density just prior to a lightning stroke (Krehbiel et al. 1979). Their measurements also showed that the electric charge on individual cloud particles of a known size was often larger than could be explained by the inductive theory of thunderstorm electrification. Limitations in the efficiency of the inductive mechanism pointed out by Gaskell (1981) possibly make non-field-dependent charge transfer processes the most important generators of thunderstorm electric fields.

Many laboratory studies of charge transfer between interacting particles have. fol- lowed from the pioneering work of Reynolds et al. (1957), whose results formed the basis

I Department of Physics, University of Colombo, Colombo 3, Sri Lanka * Desert Research Institute, Reno, Nevada 89506, U.S.A.

609

610 E. R. JAYARATNE, C. P. R. SAUNDERS and J. HALLETT

of a viable thunderstorm-charging theory. Reynolds et al. moved metal spheres on the end of an arm in a circular path through a cloud of supercooled water droplets and ice crystals and noted that the spheres generally became negatively charged with the separating crystals removing positive charge. The magnitude of the charge transferred during the collision and separation of soft-hail particles and crystals was determined to be sufficient to account for thunderstorm electric fields. Reynolds et al. performed various experiments which led them to an explanation of their results in terms of the temperature differences between the warmer hail pellet growing by riming and the colder interacting ice crystals. This temperature gradient theory was subsequently developed by Latham and Mason (1 961a,b) to account for charge transfer between ice crystals and an ice target; however, their observed charge transfer was several orders of magnitude less than that of Reynolds et al.

Hallett and Saunders (1979) measured the charge transfer to a riming rod moving through a cloud of supercooled water droplets and ice crystals. They found that in the presence of supercooled water droplets, substantial electric charge was separated but they were surprised to note that the riming rod became positively charged while the separating crystals removed negative charge. Only in conditions of very low liquid water content was the opposite charge separation noted. Subsequent to their experiments, Takahashi (1978) published his findings, which also revealed different results to those of Reynolds et al. A survey of the literature on experimental studies of charge transfer showed that a large number of laboratory experiments have been reported; some studies had as their intent the elucidation of the charge transfer mechanism itself while others aimed at simulating cloud processes. The many and varied results of these experiments will not be outlined here as they will be discussed later in terms of the results of the present experiments.

The objective of the present work is to measure the charge transferred to an ice or rime surface during interactions of ice crystals with the surface. The microphysical conditions in the cloud chamber used can be adjusted to simulate closely those regions of clouds in which particle charge separation processes occur. Thus, the charge transfers measured will result from realistic simulations of particle interactions in clouds. A specific intention is to investigate the effect of the presence of supercooled water droplets and to cover the range of experimental conditions used by other workers in order to try to resolve the apparent and real differences between their results. With this aim, experiments were performed in which ice crystals impacted with warmer or colder, evaporating or condensing, ice targets of various natures, with and without the presence of water droplets having a range of impurity content, over a range of temperature down to -25 "C.

2. EXPERIMENTAL APPARATUS AND MEASUREMENT TECHNIQUES

The experiment was conducted in a rectangular box of sheet aluminium having dimensions 1.2 x 1.2 x 0-8m3 placed in a cold room of approximately 8.5m3. The box was earthed to prevent stray electric fields from influencing the charge transfer. Figure 1 shows the essential parts of the apparatus. A cloud of supercooled droplets was formed by passing in steam from a kettle through a hole near one corner of the floor of the box. The liquid water content was measured by a psychrometric method. A sample of the cloud was drawn out at a steady flow rate through a well-lagged electrically heated metal tube so that liquid water was completely evaporated. The relative humidity of this air was then measured with wet- and dry-junction thermocouples and the liquid water content in the box calculated. The accuracy of measurement was about O.5gm-j. The amount of liquid water in the cloud could be controlled by varying the electrical power to the kettle. With the kettle working at a rate such as to produce a steady liquid water concentration of 2gm-3, the lowest cloud temperature attainable was about -25 "C. The .droplets at this liquid water content had a maximum diameter of about 30pm with the modal diameter being around 8 pm. The cloud temperature was measured to an accuracy of 0.1 K with four thermocouples placed at various points in the box. There was usually a small vertical

THE CHARGING OF SOFT-HAIL 611

H

Figure 1 . The experimental cold chamber A, amplifiers; B, target rod; C, control rod; D, thermistor; E, shielding cups; F, slip rings; G, motor; H, revolution counter; J, thermocouples; K, steam kettle; L, crystal collector plate; M, station-

ary target; N, formvar replicator.

temperature gradient of about 0.5 K m- ' in the cloud. All temperatures quoted are mean values.

Two hollow stainless steel gold-plated rods, 5 0 m m in diameter, 30cm in length, were mounted vertically on a frame attached to a central shaft which could be rotated by means of a motor placed on the roof of the cold room so that the rods moved through the cloud with their axes normal to the direction of motion. Riming took place on their leading edges. Rod speeds up to 3.6 m s- ' were used; at higher speeds the high rotational forces tended to break up the rime. Figure 2 shows rime grown on the rod at a speed of 3 m s- ' at - 10 "C. The rod speed was monitored continuously to an accuracy of about 0.05 m s-'. One rod was insulated from its supports by mounting the ends in short glass tuhes packed with paraffin and sealing wax. It was then connected to the input of a current-to-voltage converting amplifier mounted on and rotating with the central shaft. The amplifier power and output leads were taken out through slip rings. The sensitivity of the electrometer was 1 mV = 10- '' A; charge flowed to earth with a time constant of 1 s. The form of the output signal was observed on a cathode-ray oscilloscope and a trace was obtained on a pen recorder. With the rod rotating and no spurious charges present in the chamber, the background noise level was around 1 mV, so that any charge acquired by the rod was measurable provided the charging rate was greater than about 0.1 pCs-'. Earthed metal cups, 6 cm high, prevented a rime bridge linking the rod to earth.

The rime temperature was measured with a miniature bead thermistor mounted on the riming rod. The measurable sensitivity was 0-1 K. The rime could be heated electrically by means of two low power internal rod heater coils. The heater and thermistor leads were taken out through slip rings.

612 E. R. JAYARATNE, C. P. R. S A U N D E R S and J. HALLETT

Figure 2. The rime covered target rod.

Ice crystals were produced by seeding the cloud with a metal wire or small brass plate dipped into liquid nitrogen and inserted momentarily through a small opening in the box. The crystals could be viewed in a beam of light shining into the cloud through a small glass window covered with an earthed metal mesh. With the rods rotating through a cloud of liquid water content 2 g m - 3 the wire produced crystal concentrations of approximately ~ O O O C ~ - ~ while the plate gave concentrations of up to 5 0 0 0 ~ m - ~ . The crystals grew in the saturated environment, which was maintained at the expense of the evaporating droplets, to reach a maximum size of about 80-125pm before they fell out of the cloud, following which the liquid water content recovered its original value.

Throughout an experiment, a continuous formvar replicator was used to record the concentration and sizes of the cloud particles in the cold box (Hallett 1976a,b). The film was transported by means of rollers through a tube which penetrated 30cm into the cold box from outside the cold room. The cloud was sampled through an aperture of size 5.5 by 2.0mm in the side of the tube at a rate of 52mls-'. The droplet collection efficiency of the device was assumed to be the same as the collision efficiency, which was calculated from Ranz and Wong (1952) for spherical particles. The theoretical minimum size of particle which may collide with the film was about 4pm diameter, which agreed well with the minimum droplet sizes observed. The collection efficiency was unity for droplets larger than about 10pm. The smallest crystals observed were about 5pm plates and 6pm columns; the collection efficiency increased to unity for crystals larger than about 20 pm.


The crystal concentrations have not been corrected for collection efficiency losses, but because the largest charge transfer per crystal separation occurred with large crystals, no significant errors were introduced by the reduced concentration estimate for small crystals. A pull action solenoid enabled scratch marks to be made at required points on the formvar film by a remote control so that this data could later be correlated with the charging current observed on the pen recorder chart. Thus it was possible to obtain a continuous record of the rimer charging current, rod speed, cloud temperature, rime temperature and the size and concentrations of the droplets and crystals in the cloud during an experimental run.

Concurrently with the rotating rod experiment, a part of the same cloud was drawn out through a tube of diameter 2.5cm in which was placed a cylindrical brass rod of diameter 2.4mm and length 1.0cm connected to a similar electrometer. Currents from the rotating target and from the stationary target were observed on two channels of the same pen recorder. The flow through the tube could be increased to provide speeds of around 10 m s - substantially above that of the rotating rod and not accompanied by unwanted rotational effects. The suction pump was switched on only for short intervals at a time to minimize any changes in the cloud through depletion and to prevent excessive riming within the tube.

In order to measure the charges on ice crystals falling out of the cloud, a small brass plate 9cm square was placed horizontally on insulating supports on the floor of the box. When needed, the input of the electrometer was disconnected from the stationary probe and attached to the plate. The charges on the crystals gave rise to a current which was measurable on the pen recorder. To study the effects of contaminants on the separation of charge, an ultrasonic droplet generator was used to spray weak solutions of various salts into the box. The resultant drop sizes were quite large, the tail end of the spectrum extending to a diameter of 100pm at liquid water contents of 2-4gmT3, although clouds of smaller droplets could be obtained at lower liquid water contents.

3. RESULTS

(a) Charging in the presence of both droplets and ice crystals No charge was detected on the riming rod when it was rotated through a cloud

composed entirely of supercooled droplets. When the cloud was seeded, with the steam from the kettle being supplied throughout the experiment, the rime was normally electrified positively at temperatures higher than about -20°C and negatively at lower temperatures. Figure 3 shows the results of a typical run at -6-0°C and a rod speed of 2.9ms-'. The cloud was seeded with the wire at time t = 0. The maximum, initial, liquid water content, in the absence of crystals, was 2 g m-3. The droplet and crystal concentrations and crystal sizes were determined with the continuous formvar replicator. The crystal size was taken as its maximum dimension. The apparent increase in crystal concentration is due to the replicator collection efficiency increasing with crystal size. It can be seen that the charging current increased as the crystals grew at the expense of the droplets and water vapour, reaching a maximum and falling to zero as the crystals fell out of the cloud and their concentration was depleted. Non-uniformities in the shape of the charging curve in Fig. 3 are probably due to spatial and temporal variations of particle concentrations in the cloud. The short-lived peak of current within the first minute was a reproduceable feature. It is important to note that the number of droplets, taken as a rough measure of the liquid water content, became a minimum about one minute after seeding and increased thereafter while the crystals grew and fell out. Figure 4 shows the cloud particles captured by the formvar replicator throughout a typical experiment.

During the experiments it was observed that the collector plate, placed on the floor of the box, was detecting an opposite charge to that acquired by the rotating rod thus confirming that charge separation took place on the rod. When the rotation of the rod


2000-

1000-

was stopped in the course of an experiment, the current from the plate did not drop sharply to zero but decayed slowly in the time taken for all the crystals to fall out. No charge was detected when there were no crystals present in the cloud or when the cloud was seeded and the crystals grew and fell out with the rod held stationary. In the latter

Figure 3.

10

5

0

h Charg i ng Current ( PA)

1 Charge per

Event

( fc ) 1 0-1

I+

I 0-3

1

0 1 2 3

I

0 1 2 3 Time (mins)

corresponding particle concentrations and sizes observed on the formvar replicator. Temperature -6°C; rod speed 2.9ms-'; initial liquid water content 2 g n 1 - ~ .

Temporal variations of the charging current and charge separated per event together with the


A

2m E

10s 6 c 45. D 1m30s

Figure 4. The nature of the cloud particles throughout a run (from the formvar replicator). Temperature - 16.4"C; initial liquid water content 2gm-3. A, before seeding; subsequent times are after seeding.

case an average current equivalent to 10-3fC per crystal could have been detected over the noise level.

To calculate the charge separated per rebounding crystal, it was necessary to estimate the event probability, here defined as the product of the collision efficiency and the separation probability of ice crystals on the rod. The event probability was determined in some subsidiary experiments in which the current to the usual 5mm diameter moving target was compared with that to a target of l m m diameter. With the assumption of a collision and separation probability of unity for the thinner target, an upper value of 0.2 for the event probability of the thicker target was obtained. This value did not vary significantly over the range of experimental conditions used in these experiments. The calculated charge per event assuming an event probability of 0.2 is also shown on the charging current u. time graph in Fig. 3. The charge increased throughout the experiment and attained an estimated value of about lOfC for a liquid water content of 2 g m - 3 and a crystal size of about 125 pm.

Typical runs at three rime temperatures are shoyn in Fig. 5. The cloud particle concentrations and crystal sizes during runs at all temperatures were very similar to those for which data are shown in Fig. 3. For the purpose of representing the charge per event as a function of temperature it was necessary to choose a stage during each of the runs where all the other variables were the same. The instant a t which the droplets first reappeared in the light beam was chosen for this purpose because it could be easily identified visually. For convenience, this instant in each run will be referred to as the


reference stage. At a rime temperature of - 10 "C this occurred when the charging current reached its maximum positive value. At - 20 "C the current was approximately zero during this stage while at temperatures below - 20 "C it was negative. With a rod speed of 3.0ms-' and an initial liquid water content of 2gm-3 the microphysical properties of the cloud at the reference stage were very similar at all temperatures; the crystal size was about 50pm, the crystal concentration about l W ~ m - ~ and the liquid water content, estimated from the droplet concentration, about 1 g m-3. By comparing the charge per

1 I I

0 1 2 3 4 Time (mins)

Figure 5. The rotating rod charging current as a function of time at three temperatures with an indication of the variation of liquid water content throughout a run. The reference stage is marked by arrows. Rod speed,

3ms- ' .


Figure 6. The charge per event at the reference stage of runs conducted at various rime temperatures. Rod speed, 2.9m s-'; liquid water content, 1 gm-3.

event during the reference stage at different rime temperatures, Fig. 6 was drawn. The sign of the charge transfer was sensitive to temperature with the maximum, positive charging of the rime at around -10°C. As the rime temperature was reduced, charge transfer reduced until at about -20 "C sign reversal occurred.

The sign and magnitude of the charge transfer was also affected by the liquid water content of the cloud as can be seen from Fig. 5. At all temperatures, the initial liquid water content of about 2 g m V 3 caused positive rime charging. When the liquid water content was depleted by the growing crystals below a critical value dependent upon temperature, negative rime charging occurred. At -20°C at the reference stage of the experiment, the net charging current was zero with a critical liquid water content of about 1 gm-3. At - 10°C the liquid water content remained above its critical value throughout the experiment while at -25°C it had a value between 1 and 2gm-3. The positive peak at the end of the -20°C run was associated with the re-established high liquid water content but at -25 "C this was insufficient to cause sign reversal.

Even at temperatures above - 10 "C it was possible to obtain negative charging provided the liquid water content was low enough. Figure 7 shows a run at -6.5 "C with

Charging

0 -' 7 v- Time (mins)

Figure 7. A typical run at -6,S"C in which the supply of steam was removed at the indicated time. Rod speed, 2.85ms-'; initial liquid water content, 2gm-'.

the maximum, initial, liquid water content of 2 g m - 3 and rod speed 2.85ms-' in which the steam supply was cut off after the crystals had grown to a size of about 35,um. The charging fell immediately and reversed sign as the droplets were depleted giving a rime charge per event of about 1/10 of the magnitude of that just before the steam was cut OK

618 E. R. JAYARATNE, C. P. R. S A U N D E R S and J. HALLETT

No charging was detected when all the droplets had disappeared leaving a totally glaciated cloud. If the steam supply was re-introduced when crystals were still present, the rime charged negatively for a very short interval while the liquid water content was very low, then charged positively again as it increased. These results show that the negative rime charging was due to the low liquid water content rather than to the effect of evaporating or growing cloud particles and that the negative rime charging was not due to the collection by the rod of previously charged negative crystals.

The magnitude of the charge per event as a function of crystal size is shown in Fig. 8. These data are obtained from runs similar to that shown in Fig. 3. The mean slope of a number of runs with positive rime charging for the same rod speed, temperature and steam production rate, was 4.9. At a lower temperature with negative charging, the line

Figure 8.

11

10-

lo-:

itivc

C r y s t a l s i z e (prn) 3 i

10 20 50 100

The charge per event as a function of crystal size for positive rime charging at a rime temperature of -6"C, and negative rime charging at a rod speed 2.8ms-I and rime temperature -21 'C.


had a slope of 3.4. Obviously, the crystal size itself affects the charge transfer but so does the rime accretion rate. During the latter part of a run, as the crystals grew, the liquid water content increased from about 1 g m - 3 to 2gm- j , which enhanced the positive rime charging and decreased the negative rime charging leading to the different slopes of the graphs. The effect of the rime accretion rate can be removed from the size dependence relationships by taking the two results together to give an approximate fourth-power dependence on crystal size.

5.10-1

3-10-l

2-10-1

10-1

5.10-2

3-10-2 Rimer Velocity (ms-1)

I I 1 1 1.5 2 3 4

Figure 9. The charge per event as a function of rod speed at the reference stage of experiments conducted at - 1 1 "C and liquid water content 1 g m - 3

The charge per event was also found to increase with the rod speed. Figure 9 shows the charge per event determined at the reference stage of each run at - 11 "C. The mean slope of all such positive rime charging runs obtained over a range of temperature was 3.2 k 0.4. This increase is due to the effect of the impact speed on the interactions, and the increase of the rime accretion rate with velocity.

The collection efficiency of the rod for droplets was determined experimentally by weighing the amount of rime collected in a given time. In the absence of crystals, with a liquid water content of 2.0 g m- and a rod speed of 3.0 m s- ', the measured collection efficiency was about 0.1. Using the results of Ranz and Wong (1952) for spherical particles impacting at 3.0ms- ' with a cylindrical target of the same diameter as the rimed rod, this corresponds to a droplet diameter of about 8pm, in good agreement with the mean droplet diameter at 2.0 gm-3 as measured with the formvar replicator. The thermistor on

620 E. R.' JAYARATNE, C. P. R. SAUNDERS and J. HALLETT

the riming surface indicated temperature increases of between 0 and 1 K depending upon the cloud temperature and liquid water content. These increases agreed with calculations of the heat balance of the riming surface which showed that under riming conditions, the average surface temperature was elevated insufficiently to cause surface evaporation.

When positively charging rime was warmed with the internal heaters, evaporation of the surface could take place but no reversal of charging sign was observed. This suggests that the sign of charge transfer between the rime and the rebounding ice crystals, in the presence of riming, did not depend on whether the rime surface was growing or evaporating. However, in the presence of ice crystals alone, such a dependence has been observed (Buser and Aufdermaur 1977; Gaskell and Illingworth 1980). This will be discussed later. Experiments in which the rime was heated internally lead to the conclusion that the magnitude and sign of charge separated is a function of rime temperature rather than of cloud temperature or the temperature difference between cloud and rime. Figure 10 shows that heating the rime at cloud temperatures above - 10°C resulted in a decrease

'1 Charging +-, 4.

3 . I

I 2-

1 \ Rime Temperature Excess(?)

1 i 9 1 1 c Figure 10. The rime charging current at the reference stage of experiments conducted over a range of cloud

temperature with the rime heated internally to provide a rime temperature excess. Rod speed, 3 m s- '.

of the positive charging while at lower cloud temperatures, heating the ice surface first caused a slight increase in the positive charging and then, as the rime surface was heated further, the charge transfer decreased. This behaviour is consistent with the results shown in Fig. 6 in which the maximum charge transfer occurs at a rime temperature of about - 10 "C. When heated excessively, the magnitude of the charging was less than that obtained at the same rime temperature in the absence of heating, possibly due to fast evaporation which may change the ice surface structure. It was sometimes possible to reverse the negative charging of the rime at rime temperatures just below -20°C to positive by warming it by a few degrees.

Experiments with the stationary target revealed a similar charging pattern to the rotating rod in all cases. The sign of the charging was the same even when the cloud was drawn past at speeds up to 20ms- ' . At the reference stage of the experiment in the presence of riming at -10°C and a flow speed of 9*8ms-' , the mean rime charge per rebounding crystal of size 30 pm, assuming an event probability of 0.2, was about 28 fC. The magnitude of the charging was very erratic, due to the inhomogeneous nature of the cloud passing through the tube; hence the stationary target was not used for a quantitat- ive study of the charging. However, the advantage of the stationary target was that higher velocities could be used than with the moving target. In the case of riming at low liquid water contents at - 10 "C, the moving riming rod indicated a charge per event of less than

THE CHARGING OF SOFT-HAIL 62 1

-0.1 fC at its maximum speed of 3ms- ' while the stationary target detected about -2fC at 9-8ms- ' .

(b) Charging in the presence of ice crystals alone Various experiments were performed with a glaciated cloud in order to determine the

effect on the charge transfer of the target ice surface state and temperature. The results are summarized in Table 1. The charging of the moving rod due to rebounding crystals in the

TABLE 1

Surface state Sign of target

Experiment AT Target ice Crystals charge - No heating or cooling 0 E E

Radiative heating + E E Internal heating + E E Heating tube alone - E E With moist blotting paper - G G + Cool target in liquid N, - G E +

- - -

Summary of results obtained when a cloud composed entirely of ice crystals was drawn past the stationary target.

Airstream velocity, 9.8 ms-' ; cloud temperature - 10°C = T, ; rime temperature = TR : AT = TR - T, ; E = Evaporating;

G = Growing.

absence of droplets was too small to be detected due to the low impact speeds. With the stationary target, the much higher impact speeds possible enabled charge transfer to be detected. At a flow speed of 9.8ms-I with the target and cloud in thermal equilibrium, the mean charge acquired by the target per rebounding crystal of size 30pm at a temperature of about - 10 "C, assuming an event probability of 0.2, was -0.25 fC. Due to the non-uniformity of the cloud, the magnitude of the charging varied considerably. The mean charge did not vary significantly in the temperature range 0 to - 25 "C.

The stationary target could be heated radiatively to a few degrees above the airstream temperature with a 150 W white light source placed about 2 cm away from a small quartz glass window in the side of the tube. The results obtained were very similar to those of Marshall et al. (1978) in that, almost as soon as the lamp was switched on, the target charged more negatively. With a cloud temperature of about - 10 "C, the target ice temperature was about -6.5 "C at an airflow speed of 9.8 m s-'. The mean target charge per rebounding crystal of size 30 pm was about -0.5 fC. The current returned to its original value within a few seconds of the lamp being switched off. At a cloud temperature of -1O"C, with the lamp warming the target, it always charged positively when steam was re-introduced and the cloud water content was about 1 g m - 3 or more causing the target ice to grow by riming. At lower liquid water contents the target charged negatively.

A number of other experiments were carried out in which internal electric heaters were used to vary the target temperature and the ice crystals were warmed by passing them through a heated tube. These results may be summarized as follows : when ice crystals alone were drawn past a stationary ice-coated brass target it was electrified negatively at all temperatures; the negative charging was enhanced when it was heated radiatively or internally ; the negative charging was also increased when the crystal cloud was warmed by a heated tube just before it passed the target. These observations indicate that the temperature difference between the ice surface and the impacting ice crystals was not a controlling influence on the charge separation process. However, in all these cases the ice surface was in a state of evaporation.

In order to determine the effect of a growing ice target during crystal impacts, the inside of the heating tube was lined with moist blotting paper to cause the cloud passing through to become saturated. The target became positive when the tube was introduced,

622 E. R. J A Y A R A T N E , C. P. R . S A U N D E R S and J. H A L L E T T

reversing to the normal negative value as soon as it was removed. At an initial temperature of - 10°C and a flow rate of 9.8m s - I , the temperature of the air near the target was about -8°C. Under these conditions the mean charge acquired by the target per rebounding crystal of size 30pm was about +0.25 fC. The final aspect to be investigated was the effect of cooling the target with respect to the cloud, without cooling the cloud. This was achieved by dipping the ice-covered target into liquid nitrogen and quickly replacing i t in the tube. The target always became positively charged. The familiar negative charging of the target was observed after about a minute when the target attained the temperature of the cloud once again.

In these last two experiments the target was colder than the cloud as in the heated tube experiments mentioned earlier; however, the sign of the charging was opposite, confirming that the temperature difference between the two impacting surfaces is not important in the charge separation process. The results obtained for impacts with ice crystals alone are summarized in Table 1, from which i t can be seen that the parameter controlling the sign of the charge transfer is the surface state of the target which charges negatively when evaporating and positively when growing. This effect was completely masked while riming took place simultaneously, when the charge transfer was considerably greater and was controlled by the temperature and cloud liquid water content.

(c) The effect of contaminants on the charging When various materials were ignited in the cloud chamber, large numbers of cloud

condensation nuclei (CCN) were produced which caused the drop size spectrum to shift to small sizes, the maximum drop diameter being not greater than lOpm with a modal diameter of less than 4pm. which was the lower limit for detection by the formvar replicator. When a match was used to create the CCN and the cloud was seeded with a liquid nitrogen cooled wire, the charges acquired by the rotating rod and the stationary target were both negative at all temperatures. The crystals falling onto the collector plate charged it positively, indicating that charge separation was taking place on the riming rod. The sign of charge transfer could not be reversed by heating the rime with the internal heater. Similarly, negative charging of the rime occurred when CCN were introduced by burning various other substances. However, there were exceptions. Burning a small piece of polythene or certain types of paper failed to reverse the sign of charge transfer, although the droplet spectrum was changed significantly as before. This suggested that the sign reversal was not due to smaller drop sizes but was possibly a result of contamination. The rime grew from the contaminated droplets whereas the ice crystals, which grew from the vapour, remained relatively pure. No significant change in the charging was noticed when the cloud was seeded with dry ice instead of liquid nitrogen or when CO, was introduced into the cloud from a gas cylinder.

The introduction of NH, gas into the chamber resulted in strong positive charging of the rime when the cloud was seeded at all temperatures. The magnitude of this positive charge increased with decreasing temperature. With a maximum liquid water content of 1.9gm-3 and a rod speed of 3 ,0ms- ' , the positive charge acquired by the rime per rebounding crystal of size 50pm was as high as +2OfC at a rime temperature of -22 "C. NH, readily dissolves in water and the crystals grew from the vapour so that both the rime and the rebounding crystals would have been contaminated. However, as the concentrations were not known, it was not possible to determine which of the two surfaces was more contaminated.

An ultrasonic droplet generator (atomizer) was used to form a cloud of droplets from pure water and weak salt solutions. The droplet sizes ranged from 10 to 100pm in diameter with a modal value of about 25pm. The liquid water contents were determined with the psychrometer by the usual method and values up to 4 g m - 3 were used. For pure water, the pattern of charge transfer was similar to that with the steam-produced cloud; when a cloud of liquid water content of approximately 2 .0gm-3 was seeded, the rime acquired a positive charge at all temperatures above about - 18°C and a negative charge


at lower temperatures. With the rotating rod, the estimated charge per event at a given temperature and rod speed was greater than with the steam-produced cloud for the same liquid water content by a factor of as much as two, probably due to the greater collision efficiencies of the larger droplets.

When slight traces of impurities were added to the water, the charging pattern changed significantly. With weak solutions of NaCl, in the range lop5 to IOv3N, there was a small negative current to the rime in the absence of any crystals. When the cloud was seeded the rime charged more negatively. The magnitude of this charge transfer increased with decreasing temperature. The current to the rime at the experiment reference stage with a liquid water content of 1 gm-3 and crystal size of 50pm is shown as a function of rime temperature for various NaCl solute concentrations in Fig. 11. The ice

! 0 .-

- I .

- 8 -

-10-

2.16~~

Figure 1 1 . The charge per event at the reference stage as a function of rime temperature when the droplets in the cloud contained dilute (NH,),SO, or NaCl solution; rod speed, 3ms- ' .

crystal concentrations were determined by collecting them on formvar slides and found to be similar to those with the steam-produced cloud. The estimated rime charge per rebounding 100pm crystal, using a 5 x N NaCl solution at a rod speed of 3.0ms-' and a liquid water content of 2.0gm-3, was about -2OfC when the rime temperature was about - l O T , increasing to as high as - l00fC at -20 "C. The corresponding values with a 2 x 10--'N NaCl solution were about -8 and -6OfC respectively. A 2 x 10-'N NaCl solution was sufficient to keep the rime charging negatively at all temperatures. When the concentration was reduced to about 8 x 10-6N, the rime acquired a positive charge at - 5 "C and a negative charge at - 15 "C. With NH, salts the charging was more complicated. Figure 11 shows the results obtained with (NH,)$O,. It is seen that at temperatures above about - 8 "C increasing the concentration of solute decreased the charge transferred to the rime, while at lower temperatures it was increased. With a further increase in solute concentration to 10-3N, the rime charged negatively at temperatures above - 11 "C. NH,OH showed a similar result of the same magnitude while


2-

NH,Cl solutions showed a similar result but with reduced charge transfer for the same solute concentrations.

In another set of experiments, solutions were prepared by mixing equal volumes of two equi-normal solutions of NaCl and (NH,),SO, each of which alone produced an increasing charge transfer at lower temperatures but in the opposite sense. The current to the rime was negative at all temperatures until the concentration of each solute was decreased below about N. At lower concentrations the rime charged positively above a critical temperature and negatively at lower temperatures. The critical temperature decreased as the salt concentrations were reduced, approaching - 20 "C when the water was free of any solute.

Cloud Water Content (gm-3)

4. DISCUSSION

The set of experiments just described was performed over a wide range of cloud conditions covering many of the situations used in studies by other workers. Most impor- tantly, the cloud particle concentrations and sizes, which changed throughout an experiment, were monitored continuously by the formvar replicator giving confidence in the calculated values of charge transfer per separation event. Many of the other studies have relied on spot measurements of these variables, or have averaged them throughout an experiment. Therefore it is difficult to compare particular values of charge transfer obtained with those produced here. However, it is possible to relate them to the general trend of the present results illustrated in Fig. 12. The present results indicate that there are

/ 1 - POSIT1 VE

NEGATl VE

1 -

Temperature (OC) Ot 0 -10 -20

Temperature (OC) I 1 1 I

-20 0 0 -10

Figure 12. Positive and negative rime charging zones as a function of cloud liquid water content and rime temperature.

two main charge transfer regimes. Firstly, when crystals alone separate from an ice target the target becomes negatively charged when its surface is evaporating, but positively charged when growing by vapour diffusion. A second and far more powerful mechanism is involved when crystals interact with a riming target. Then the sign of the charge transfer is controlled by impurities and the temperature and liquid water content of the cloud. By making the distinction between these two charge transfer regimes when comparing results with other work, some of the conflicts and discrepancies may be resolved. For example, Reynolds et al. (1957) measured charge transfer of -16OfC to a riming target per ice crystal collision, while Latham and Mason (1961 b), who bombarded an ice target with ice crystals alone, separated only - 1.6 x lO-'fC. These extreme results have been the source of much controversy ever since (Reynolds and Brook 1962; Mason and


Latham 1962; Latham 1965; Church 1966). An attempt to reconcile the results was made by Church who performed experiments

similar to those of Reynolds et al. and found results similar to those of the present work. For example, using a probe on a rotating arm, he found that at temperatures above -20 "C, the probe was electrified positively when the steam supply to his ice crystal cloud was maintained throughout an experiment. With a low liquid water content cloud the probe was electrified negatively. Experiments in which the target. was heated or contained NaCl also gave similar results. Church, Reynolds et al., and Latham and Mason attempted to explain all their results in terms of the temperature gradient theory, but the present work shows that this theory is not appropriate because it cannot account for the temperature dependence of the rime charging and the charge reversal temperature.

Reynolds et al. (1957) obtained negative charging of their target ice with crystals and high liquid water contents. The temperatures used were not stated, but the refrigerator used could be cooled down to -25°C. These results, which fit in with Fig. 12, suggest that their experiments were most probably conducted close to this temperature. However, they observed positive charging of their target a t low liquid water contents, a finding which was confirmed by Takahashi (1978) who, in a somewhat similar experiment, detected tiny broken rime branches in his cloud chamber during this charging phase. He suggested that the rime branches were broken off by impacting ice crystals and that a separation of charge occurred during this process, the target becoming positive. No such positive electrification of the rime at low liquid water content and low temperature was found in the present study. The metal spheres used by Reynolds et al. and by Takahashi were moved through the cloud on the end of arms at speeds close to 9 m s-', giving rise to rotational accelerations of 125 g and 75 g, respectively. The corresponding figure in the present experiment was about 6 g which was probably insufficient to break off any rime and is more representative of the accelerations experienced by tumbling soft-hail particles. It was possible to use speeds up to 20ms-I with the stationary target in the present experiments, but no positive charging was found with low liquid water contents at temperatures down to -22"C, suggesting that high rotational forces may cause spurious effects.

Takahashi did not observe negative rime charging at temperatures above - 10 "C, a result which can also be explained in terms of the breaking of rime branches under high rotational forces which may favour positive rime charging. His sign reversal temperature at a liquid water content of l-2gmP3 was - 10°C whereas in the present study it was around -20°C. Takahashi measured the liquid water content by weighing the rime and crystals collected on a rotating rod but did not correct for the presence of the crystals so his values may considerably overestimate the true liquid water content. He had outside air circulating through the chamber all the time from which the droplets in his cloud condensed. Bringing outside air into the present experiment caused a decrease in the positive rime charging, possibly due to the impurities introduced. Similar effects may have contributed to Takahashi's higher charge reversal temperature. As in the present work, Reynolds et al. and Takahashi found that when the droplets and hence the rime were contaminated with NaCl the target charged more negatively during ice crystal collisions. Takahashi also found the same results with (NH&SO,. This is consistent with the present results if Takahashi conducted his experiment at a temperature above about - 10°C.

There is agreement between the present and previous work that only a small charge transfer occurs in the presence of ice crystals alone, that the effect of warming the target under these conditions, or with a low liquid water content cloud, is to cause negative target charging, and that the effect of cooling the target with respect to the impacting cloud is to cause positive target charging (Reynolds et al. 1957; Latham and Mason 1961b; Church 1966; Marshall et al. 1978; Takahashi 1978). However, Buser and Aufder- maur (1977) measured the charge separated when frozen drops of diameter 10-40pm rebounded off metal and ice targets at a speed of 10 m s - at -45 "C. They found that the


charging of different metal targets was related to their work functions. When all other factors were held constant, the charge transfer was found to increase as the fourth power of the impact velocity in the range 2-20ms-'. It was also found that an ice surface growing by deposition charged by + 2.3 fC per collision while an evaporating one was charged by - 2.0 fC per collision. This led Buser and Aufdermaur to postulate the existence of a contact potential on ice which changed with the state of the ice surface. In an environment just saturated with respect to ice, a heated ice surface would evaporate while a cooled one would grow by vapour diffusion. The contact potential theory predicts a step function change in the charging when ice crystals rebound off an ice target in the two cases, whereas thermoelectric theory predicts a linear variation with the surface temperature excess of the ice target. Marshall et al. measured the charging of an ice-coated probe in a wind tunnel when clouds of vapour-grown ice crystals of mean diameter 10 pm were drawn past at various speeds. When the probe was warmed radiatively the charging increased negatively and attained a saturation value when the temperature elevation was above 1 K. This is not explicable in terms of thermoelectric theory. The charging increased as roughly the third power of the airstream velocity in the range 3 to 9 m s- '. Even at an impact velocity of 18ms- ' the charge transferred to the heated target was typically only of order 1 fC, which is insufficient to explain thunderstorm electrification. Gaskell and Illingworth (1980), who used an apparatus similar to that of Buser and Aufdermaur, found that when frozen drops of diameter lOOpm were made to impact on a cylindrical ice target at a speed of 8 m s - ', the target acquired a typical charge of about - 15 fC per collision when in a state of evaporation. Targets maintained at a temperature 1-5 K below the ambient temperature acquired large positive charges, sometimes as much as +3OOfC per collision. Targets cooled by these amounts with respect to the ambient temperature charged negatively if maintained in a state of evaporation. This confirmed that the temperature difference was not a controlling parameter. The charge per collision increased with increasing impact velocity and frozen drop diameter, probably due to an increase in contact area between the two particles. In the presence of low riming rates, with liquid water contents in the range 0.05 to 0 ~ 8 5 g m - ~ , it was found that the average charge acquired by the target due to 100pm frozen drop collisions was positive above - 10°C and negative below. The results of the present work with crystals and those of Gaskell and Illingworth with frozen drops show similar temperature-dependent charge transfer suggesting that a similar mechanism may be acting, although the magnitudes may well be different due to the different momenta, interaction times and character of the interactions at the rime surface.

It is evident that certain physical properties of the surfaces of interacting ice particles control the charge transfer between them. This study has attempted to determine reliable charge transfer values for realistic cloud situations rather than to explain the measured values in terms of a complete theory. It has been possible to show that temperature differences do not drive the charge transfer and that in the non-riming case, the sign of the charge transfer is linked to the evaporation or growth of the target ice, but that when riming occurs the sign of the charge transfer is not so linked. It was thought possible by Buser and Aufdermaur (1977) that the contact potential of ice may provide the driving mechanism, but Caranti et al. (1980) found no difference between the contact potentials of growing and evaporating ice. However, they did note that a previously rimed surface acquired a potential of up to -400mV with respect to an unrimed surface. The potential was temperature dependent down to - 15 "C where it reached its maximum value and decayed slowly over 24 hours. Contamination of the rime with N solutions of NaCl, NH,OH or H F made no difference to the potential. If a vapour-grown ice crystal with a different contact potential was to interact with such a rimed surface, then charge transfer would take place. However, the value of the crystal contact potential is, at present, hypothetical.

There is a prima facie conflict between the interpretation of the results of Caranti et al. in terms of contact potentials and the results of the present work in that the contact


potential is not affected by the surface state or by contamination of the target, both of which affect the charge transfer, and that the rime contact potentials persist for a few hours after the formation of the rime whereas in the present experiment, the charge transfer decreases to negligible values when riming ceases.

The rapid fall of the charging current as riming ceases gives strong evidence for the importance of the transient surface properties of the rime. When riming takes place, the sign of charge transfer due to ice crystal collisions depends on the rime temperature and the liquid water content which controls the rime accretion rate. These parameters may well control both the freezing rate and the direction of propagation of the freezing front in drops freezing on the riming surface. The motion of the freezing front will concentrate impurities at the surface or away from the surface depending on the freezing direction and the speed of the front; charge of either sign may be differentially segregated in liquid or solid regions of the interface. Increasing the liquid water content at all temperatures, even during negative rime charging below - 20 "C, resulted in the charging current changing in the positive sense. This implies that the change is not due to the rime accretion rate alone simply causing more charge transfer due to more interaction sites on the target, but is related to the nature of the rime surface in some way. Higher temperatures, larger droplet sizes and higher impact velocities of the droplets all lead to more dense rime (Macklin and Payne 1968). In the present experiments, higher temperatures and more liquid water also resulted in more positive charging of the rime and would have increased the rime density. Changes in the opposite sense give lower density rime and these resulted in more negative charging of the rime. Thus, real physical and chemical differences can result at the riming surface at different temperatures and liquid water contents which possibly can control the sign and magnitude of the charge transfer.

5. APPLICATION TO THUNDERSTORMS

In-cloud measurements have shown that there is a mix of soft-hail, ice crystals and supercooled water droplets in regions of clouds where electrical activity has been identified. These laboratory studies have shown that such a combination of particles can produce substantial charge separation. Observations in the absence of riming are not likely to be important in natural thunderstorms, where most of the electrification occurs in regions of fairly high liquid water content (> 1 gm-3) and strong convective activity. Even in very low liquid water content regions the electrification may be insignificant. The laboratory riming experiments indicate that the charge reversal temperature of - 20 "C moves to higher temperatures when the droplets carry small traces of the most commonly occurring contaminants. Most of the data on the chemical composition of cloud water have been obtained from the analysis of rainwater collected at the ground where estimates of Na+ and C1- concentrations vary from 10-4N over oceans to 10-'N over land (Junge and Werby 1958; Petrenchuk and Selezneva 1970; Miller 1974). The NH: concentration has generally been less than that of NA+ and C1-. Wisniewski and Cotton (1974) collected cloud water samples from an aircraft at the base of a cloud and found Na+ and C1- concentrations of approximately 5 x N inland. Takahashi (1963) determined the concentration of salt ions in water from melted soft-hail particles and found N a + and CI- concentrations of about 10-4N while the NH: concentration was almost two orders of magnitude smaller. Cloud water of composition 10-6N each of NaCl and (NH4)2S0, produces a charge reversal temperature at about - 10 "C for a liquid water content of 1 gm-3. Increased or reduced impurity concentrations lead to higher or lower charge reversal temperatures, respectively.

The thunderstorm-charging process outlined below results, through gravitational separation, in the development of the negative charge centre at the level of the charge reversal temperature, TR. Electric field change measurements by Krehbiel et al. (1979, 1980) have shown that the negative charge centres often lie between the -9°C and -25 "C isotherms. Values of TR have been found within this range in the current laboratory measurements. At temperatures below TR , soft-hail pellets will become negatively


charged during riming while at higher temperatures they will become positively charged. There will be a predominance of negatively charged particles in regions of updraught close to the reversal temperature level due to negatively charged soft-hail falling from above together with negatively charged crystals being transported from below. Inter- actions at levels colder than TR will produce positively charged crystals which will be carried aloft. Having fallen past the reversal level, a soft-hail pellet will undergo collisions with crystals which may eventually neutralize any negative charge acquired aloft and produce a positively charged particle. This process may explain the small positive charge centre sometimes observed near the base of a thundercloud, but only for situations in which the cloud water is free of significant quantities of contaminants such as NaCl which move TR to warmer levels. There is no requirement in the process described here for falling negatively charged particles to stop their motion at the level of the negative charge centre, a requirement that Telford (1982) holds against particle theories of thunderstorm charge generation.

Illingworth and Latham (1 977) developed a one-dimensional model of thunderstorm electric field development and showed that a non-inductive ice-ice mechanism could produce breakdown fields within the time available in a typical thundercloud if the average charge per collision was 140 fC. Rawlins (1982), using a three-dimensional model, obtained a requirement of between 10 and 65fC for a similar ice-ice charging process. The existence of a charge reversal temperature level within the interaction zone can now be included in such models together with the important effects of temperature, crystal size, impact velocity and cloud liquid water content on the charge separated per event. The present experiments showed that the charge acquired by a riming ice target per rebounding crystal has a magnitude approximately proportional to the velocity of impact cubed and approximately to the diameter of the particle to the fourth power. These relationships, when taken in conjunction with data from specific experiments, can be used to provide estimates of charge transfer in thunderstorms. In the absence of information on the event probability, theoretical models have, to date, assumed a collision and separation probability of unity. In order to be compatible, the presently obtained charge per event can be transformed into an average charge per collision by multiplying by 0-2. When the data are extrapolated to thunderstorm conditions, charge transfers per collision of the order of lOOfC are easily attained. The experiments showed that when the cloud consisted of 2 g m - j of droplets contaminated with NaCl in a concentration of 5 x lO-'N at -2O"C, a lOOpm crystal impacting at 3ms- ' charged the rime by about -20fC per collision. This value would be enhanced for larger crystals and higher relative velocities. These predicted values of charge transfer are adequate, when multiple collisions are taken into account, to explain the magnitudes of the charges observed on cloud particles and are also compatible with the values required by theoretical models to account for the observed electric fields in thunderstorms.

6. CONCLUSIONS

The electrification of both an ice-coated rod moving through a cloud, and a stationary ice-coated target past which a small volume of the cloud was drawn simultaneously, were investigated under various conditions. With a cloud of 30pm ice crystals and no supercooled drops, an ice surface gains negative charge when evaporating and positive charge when growing. Charging rates are less than 0.25fC per separation for 30pm crystals impacting with a velocity of about 10m s-'. The temperature difference between the target ice surface and the crystals was not a controlling parameter, which rules out the thermoelectric effect as a responsible mechanism.

In the experiments with liquid water present, the charge transfer was much greater than that with ice crystals alone. With a liquid water content of l g m T 3 , pure rime charged positively when it was warmer than -20°C and negatively when colder. The charge reversal temperature decreased to about - 25 "C for 2.0 g me3 liquid water content. Heating the rime did not affect the charging significantly provided the liquid

T H E CHARGING OF SOFT-HAIL 629

water content was greater than about 1.0gm-3. With the rod moving at a speed of 3.0ms-I through a cloud of liquid water content l .0gm-3, at a rime temperature of - 10°C a rebounding crystal of diameter 50pm charged the rime by about + 1 fC. Doubling both the liquid water content and the crystal size together increased this to about + tOfC.

These results suggest that the charge transfer mechanism when ice crystals bounce off a riming particle is different from that when i t is not in the process of being rimed. Until recently it was thought that riming was important only in warming the hailstone. Hence, many laboratory workers in the past used ice crystals rebounding from an ice target which was warmed artificially in order to simulate the warming effect of riming. This was probably the reason for contradictory results between the riming experiments of Rey- nolds, Brook and Gourley and those of Latham and Mason, who used a heated ice target with no riming.

Ice crystals rebounding from rime formed from droplets contaminated with NaCl charged it negatively at all temperatures when the concentration of the solution was greater than about 2 x N; the charging increased with increasing concentration. With NH, salts the rime charged negatively at temperatures above - IO'C, becoming increasingly positive as the temperature decreased.

The charging current to the rime reversed from positive to negative as the temperature and the liquid water content were decreased, which leads to the possibility that the charging mechanism is controlled by the detailed freezing process of the droplets or the structure and density of the rime.

The results suggest that in thunderclouds, soft-hail particles become negatively charged above a certain altitude, determined by the charge reversal temperature, and the separating crystals carry the positive charges in the updraught to the top of the cloud. The soft-hail particles carry the negative charge downwards past the charge reversal temperature level when they begin to charge positively due to further ice crystal collisions. The maximum negative charge concentration in the cloud is located at the altitude of the charge reversal temperature. The crystals rebounding from soft-hail particles at lower altitudes will be carried in the updraught and enhance the magnitude of the negative charge region. If a particle is completely neutralized before it falls out of the cloud it may acquire a net positive charge contributing to the commonly observed subsidiary positive charge centre at the base of the cloud.

ACKNOWLEDGMENTS

This work was supported in part by the Atmospheric Sciences Division of the National Science Foundation (Washington, DC) under Grant No. ATM79-20399 and in part by the award of a Commonwealth Scholarship to Dr Jayaratne.

Buser. 0. and Aufdermaur. A. N

Caranti, J. M. and Illingworth. A . J.

Christian, H., Holmes, C. R. , Bullock, J. W., Gaskell, W., lllingworth, A. J . and Latham, J .

Church. C. R.

Gaskell, W

Gaskell, W., lllingworth A. J., Latham, J. and Moore, C. B.

1977

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I980

I966

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Documents

Laboratory studies of the charging of soft-hail during ice crystal interactions