Physics Review: Electricity

Physics Review: Electricity Electron: Small, mobile, only loosely connected to atoms me=9.1x10-31 kg qe=-1.6x10-19 C Conservation of Charge: We can neither create nor destroy charge If we observe regions of charge, it had to come from somewhere If we observe regions of charge disappear, it had to move somewhere Total charge stays the same, but it can move around

Physics Review: Coulomb’s Law The force exerted on one particle by another is proportional to the magnitude of each of the charges, and inversely proportional to the separation distance squared r q1 q2 ε=8.85 x 10-12 C2 m-2 N-1

Physics Review: Electric Fields Electric Field: Vector field created by electrical charges, points away from positive charge toward negative charge Depicts the force a charge placed in the field would feel (E=F/q) Units: N/C=V/m

Global Circuit Lower atmosphere is weak conductor It is well known that there is a conduction current to ground in fair weather to maintain this capacitor Has been suggested that thunderstorms drive the global circuit + - Rc Fair weather E field, 120 V/m at the ground.

What is the relaxation time of the global circuit? This is the e-folding time for the Fair Weather electric field. The time required for the E field to decrease by 1/e. It can be shown using Ohm’s Law and Gauss’ Law that the E folding time is given by RC, a time constant, the resistance of the atmosphere times the capacitance of the atmosphere. Furthermore, it can be shown that RC = /, where  is the permittivity and  is the conductivity. 8.85 E –12 Farads m-1, 20 E –14 Mhos per meter. RC = 500 seconds, vary rapid decrease on E field due to “lossy” dielectric. Without thunderstorms, fair weather field would rapidly dissipate.

Thunderstorms: Thunderstorms are storms that produce thunder (and thus, lightning) Thunder: generated by the rapid expansion and subsequent compression of heated air in the lightning channel

Storm charge structure Dipole/tripole Vertically separated, oppositely charged regions Screening layer (layer of opposite polarity on upper cloud boundary) Structure can be more complex outside updrafts or in stratiform precipitation

Observations of Storm Electrification

Observations of Storm Electrification Stolzenburg et al. (1998)

Typical characteristics of charge structure 1. Negative charge usually dominates lower regions in temperature ranges warmer than -25ºC 2. Positive region above and below negative charge. This is a normal polarity tripole. 3. Deviations from basic model exist, “inverted” tripole Screening layers exist, can be a few 100 m thick on cloud top and bottom edges Most small negative ion charge below thunderstorm produced by point/corona discharge

How does this charge structure develop?

Charge Separation model 1. The average duration of precipitation and electrical activity from a single cell storm is 30 min 2. Charge separation in thunderstorm can reach several hundred million volts and may transfer 10 or more C of charge to the ground Resulting current from a single bolt could light a city of 200,000 people for 1 minute 3. Charge is bound in volume between about 0ºC and -40ºC 4. Closely associated with precipitation formation in most cases—ICE!!!

Side note: Hydrometeor reminder Hail: Dense, fall speeds up to 50 m s-1, diameters > 5 mm “wet growth”: Particles collect so fast that latent heat keeps liquid water layer that freezes from inside out “dry growth”: large size, but not collecting appreciable for latent heat to dominate Graupel: “soft hail”, small fall speeds (1-3 m s-1) Growth by riming (on a snow crystal) Riming: Accreted particles freeze rapidly to graupel as distinct particles

Cloud Electrification Theories

Electrification Theories 1. Charge placed on hydrometeors -Such that its ability to move under the influence of electrical forces is drastically reduced 2. Charge of one sign must be kept isolated from opposite charge or be moved by wind & gravity to create regions of net charge 3. Amount of charge carried by single hydrometeor is limited

Precipitation Based Air Motion Based Williams, Scientific American

Convective Charging Theory -Normal fair-weather E field establishes + charge concentration in lower troposphere, which when carried by updrafts to the top of storms, attracts - free ions, which are then carried down by downdrafts on cloud edges -Charge is separated by the up- and downdrafts -Found by Chiu and Klett (1976) that this cannot produce sufficient cloud charging

Inductive Charging General overview: Existing electric field to induce charge on surface of hydrometeors Previously uncharged hydrometeor will acquire charges of opposite polarity on opposite surface of hydrometeor Particles collide: large ‘precipitation particle’ usually acquires negative charge, smaller particle gets + Charge then separated by differential sedimentation of particles in storm + - E

Inductive Charging Rebounding particle-particle collisions Need high collision efficiency, low coalesence efficiency Precipitation and cloud particles become polarized in ambient E field (Sartor, 1954) Some charge transferred from precipitation particle to cloud drop Cloud drop carries charge away and leaves excess of opposite charge on precipitation particle

Inductive Charging Must meet 3 conditions: Colliding particles must separate (raindrops and small liquid cloud drops coalesce readily) Contact time is long enough for charge to flow from 1 particle to another -Number of studies (Illingworth and Caranti 1985, Takahashi 1978, and Gaskell 1981) showed that little charge is transferred from ice crystals and larger un-rimed ice particles Cannot increase the amount of charge in 2 neighboring oppositely charged regions unless by collisions i.e., upward moving particles collide then continue upward to contribute to upper charge in storm, and same with downward particles

Inductive Charging Problem: Cannot explain initial intensification of electric field Need to be effective in fair weather Need initial electric field to induce charge in particles Thus, usually hypothesized for intensification of electrification, not how electrification begins

Non-inductive charging Does not require hydrometeors to be polarized by ambient E field Several different theories fall under this category

Basic premise is that large and small ice particles along with supercooled droplets, collide and rebound in a cloud, with charge of opposite sign being retained on the graupel and small ice particles, respectively. Graupel charges negatively under certain conditions and positively under other conditions. Williams, Scientific American

Non-inductive charging Charge is separated by motions in the storm which move hydrometeors around Gravity Convection (free and forced)

Non-inductive charging Non-inductive, graupel-ice mechanism (Reynolds et al., 1957; Takahashi, 1978) Has been shown in both observations and lab to be capable of electrifying clouds to point of electrical breakdown Charge is separated by collisions between graupel and liquid water (LW) droplets and/or ice particles with no LW. Magnitude of charge transfer is much higher when LW is present compared to when it is not.

Non-inductive charging Exact mechanisms for this type of charging are not completely understood Lab experiments have shown that magnitude and sign of charge are dependent on: Temperature (Takahashi, 1978) Liquid water content (Takahashi, 1978) or equivalent liquid water content (Saunders et al., 1991; Saunders and Brooks, 1992) ELWC accounts for drops swept around graupel that do not collide with graupel particle Possibly size of ice crystal, impact velocity and contaminants in water particle (Jayaratne et al., 1983 and Keith and Saunders, 1990)

Takahashi, 1978, JAS 10-4 esu = 33 fC Femto = 10-15

Charge reversal Charge reversal occurs either by changing LWC or rimer velocity (i.e., rime accretion rate) Occurs between about -10ºC and -20ºC

Non-inductive charging Saunders et al. (1991) and Takahashi (1978) agree fairly well, though depends on experiment design Some discrepancies: Charge transfer at LWC large enough to cause “wet growth” of graupel Saunders and Brooks (1992) found a significant reduction Takahashi (1978) shows still + charge transfer Cannot exactly reproduce Takahashi findings LWC overestimated by his experiment design? At medium LWC and warm T: Brooks and Saunders (1995) noted that charge transfer appeared to be large function of supersaturation with respect to ice Supersaturation w.r.t. ice could affect polarity of transfer

Non-inductive charging Agreements about non-inductive charging Significant charging occurs only when larger particle is rimed and at least small amounts of cloud LW are present Large LWC, graupel becomes + Smaller LWC, graupel acquires - charge -Responsible for main charged regions of thunderstorms? At freezing T~0ºC graupel charges + for most LWC

How do hydrometeors charge non-inductively?

Properties of Water

Electrical properties of water How do hydrometeors get non-inductively charged? 1) Water is polar molecule Permanent dipole moment Thus, molecules can align in external E field So, partial alignment in raindrop (becomes dielectric) Net result: reduced E field inside drop and increased E field outside droplet + - - + - +

Electrical properties of water 2) Electric double-layer A dipolar layer exists just inside an interface between two substances Most studies have shown that the - layer is on the outside, + layer on the inside (Fletcher 1962, 1968) Charging from double layer: More of outer layer charge removed than inner layer, leading to excess of inner charge after collision 2 ice particles rubbed together will result in one shearing more charge from the upper layer than from the lower layer of the other particle Air - Water/ice - - + - + + - + + - - + - + - - + + + + +

Electrical Properties of Water Quasi-liquid layer Air-ice interface behaves like a thin film of water Baker and Dash (1994): Particles can exchange material. Mass flows from: Thick to thin QLL - - - + + - - + - + + - - + - - - - - - + - - + + - - + - - - - +

Electrical Properties of Water Quasi-liquid layer Furukawa et al. (1987) and Dong and Hallett (1992) showed this only occurs > -4 °C, but Dash (1989), Golecki and Jaccard (1978) and Elbaum et al. (1992) showed it could be ultra-thin layers down to -30 ºC Dash et al. (2001): Collisional melting, 40 nm thick layer equalizes charge in 1 µs, collision lasts 0.1 ms Charging occurs via the transfer of negatively charged ions - - - + + - - + - + + - - + - - - - - - + - - + + - - + - - - - +

Non-inductive charging: Conclusions Considered to be the main charging mechanism in thunderstorms Rapid charge transfer can occur at interface Operates most effectively with high concentrations of vapor-grown ice crystals that collide with large, rapidly falling rimed ice particles (graupel/hail)

Williams et al. 1994, JGR Particle growing most rapidly by vapor deposition gains positive charge, as it has the highest surface density of negative ions and loses them in collisions Caption is wrong, open circles denote positive charging on graupel, dark circles indicate negative charging of graupel!

Saunders 2008

Melting Charging There is consistently observed a significant charge layer near 0 °C in stratiform precipitation Can be negative or positive – usually positive Usually requires radar bright band and isothermal layer (Shepherd et al. 1996) Lightning that initiates within stratiform precipitation almost always does so near the melting level (Lang and Rutledge 2008; Lang et al. 2010)

Melting Charging Two possible processes to explain observed E-field data (Marshall and Rust 1993; Stolzenburg et al. 1994; Shepherd et al. 1996) Both involve the shedding of water droplets by melting ice; shed droplets remain near 0 °C while oppositely charged precipitation falls below Non-Inductive (Drake 1968): Convection in a melting ice sphere produces negatively charged droplets that are ejected from bursting air bubbles at the surface Inductive (Simpson 1909): Sign of charge on shed droplets depends on sign of electric field; e.g., positive field leads to positively charged droplets and negatively charged precipitation