03:03:59 UT, 2000 frames/second

The fourth high-speed video trigger on October 7 was obtained at 03:03:59 UT. It was also the first trigger on the 7th to successfully capture a sprite. The observations were of a cluster of carrot sprites at a video rate of 2000 frames/second. The sprites were associated with a 30 kA +CG at 332 km range. Development of the cluster is shown in Figures 5.2-5.3.

Figure 5.2: Initial development of a cluster of carrot and columniform sprites, at a speed of 2000 frames/second. The sprites initiated at different times within the first several frames and all began with a columniform shape, the downward (positive streamer) portion of which often split into tendrils. An upward divergent carrot shape began to emerge in some of the sprites as negative streamers were initiated in the latter frames from regions through which the positive streamers propagated. The vertical bar denotes the altitude in kilometers directly above the parent +CG, with tick marks corresponding to 10 km height intervals.

Figure 5.3: Continued development of the carrot and columniform sprite cluster of Figure 5.2. Additional upward developing streamers are evident in frames j-m. All of the sprites gradually decayed after frame m.

The start of light integration for the first frame (Figure 5.2a) was at 03:03:59.8067 UT. The integration of light in the frame is not performed simultaneously, as discussed in Appendix B.4.2. Rather, a video frame recorded at 2000 frames/second is composed of 6 horizontal blocks each of which is integrated discretely.

Figure 5.4 shows the first four frames of the sprite cluster development (Figures 5.2a-d) with the pixel intensities stretched such that faint sprite features are readily visible. The horizontal lines correspond to the location of block boundaries, with the uppermost block (block 1) excluded from the images. The block boundary locations will factor into the velocity estimates of vertical sprite development, since the time elapsed between frames depends on the block number. The start and stop times of light integration for the high-speed video blocks is shown in Figure 5.5 relative to electric field and photometer data. Frame $a$ is delayed by $\simeq$4 ms after the +CG.

Figure 5.4: Image sequence corresponding to Figures 5.2a-d, with the pixel intensity modified to emphasize fainter features. The block boundary locations are indicated by the horizontal bars. The seven sprites which are visible by frame $d$ are denoted with letters. The center sprite, D, was the first to form, as evidenced by the single camera pixel illuminated in frame $a$. All of the sprites developed simultaneously upwards and downwards, and tendrils branched downwards from sprites B, D, and F.

Figure 5.5: The electric field and photometer data for the 03:03:59 UT event. The photometer signal is coincident with a small-amplitude slow electric field change. The start and stop times are shown for the different light-integration blocks (see Appendix A.1) of frames in Figures 5.2-5.3.

Seven distinct sprites formed within the first four frames. The sprites are labeled from left to right in frame $d$ of Figure 5.4. The vertical bar denotes altitude in kilometers MSL directly above the parent +CG stroke with the tick marks indicating 10 km height intervals.

Sprite D apparently formed first, as evidenced by the single sensor pixel illuminated in the first frame. If the plan distance to the sprite were the same as to the parent +CG, then this luminous spot would have been at an altitude of 79.3 km MSL. The maximum altitude of sprite D would have been $\simeq\,$98 km MSL (see frame h of Figure 5.2) if the sprite was located at the same plan location as the +CG. Triangulation studies of sprites indicate that the maximum altitude generally does not exceed $\simeq\,$93 km MSL (Sentman et al., 1995). Thus, it is likely that the plan location of sprite D was closer than that of the +CG. In Chapter 3, an upper terminal altitude of 87 km MSL was used to determine the most likely range of sprites. The 03:03:59 UT sprites were brighter than average, so the terminal altitude was probably higher than 87 km. Unless stated otherwise, the height and velocity estimates in this section will be based on the assumption that the terminal altitude of each sprite was $\simeq\,$90 km MSL.

The range to sprite D would have been 306 km for a 90 km MSL terminal altitude. With this assumption, the plan location of the sprite would have been at least 26 km away from the parent +CG stroke location. This is a reasonable distance since triangulated measurements of sprites show that their plan location can be as far as $\simeq\,$50 km away from the parent +CG (Lyons, 1996; Wescott et al., 1998) (also see Chapter 3).

The initial luminosity from sprite D was at $\simeq\,$72.9 km MSL altitude. The sprite developed both upward to $\simeq\,$78.0 km MSL and downward to $\simeq\,$68.4 km MSL in frame $b$ with the minimum altitude barely visible as a single illuminated sensor pixel at the top of block 5. The maximum altitude of the sprite in frame $b$ was one block higher than the starting point in frame $a$. Thus, the time elapsed for the upward development was $((6\!-\!1)/6)\times0.5\,=\,0.417$ ms. The average upward development velocity of sprite D in frame $b$ was therefore $((78.0\!-\!72.9)\times10^3)/(0.417\times10^{-3})\,=\,1.2\times10^7$ m/s. The minimum altitude was one block lower than the starting point with a time elapsed for downward development of $((6\!+\!1)/6)\times0.5\,=\,0.583$ ms. The average downward development velocity of sprite D in frame $b$ was therefore $((72.9\!-\!68.4)\times10^3)/(0.583\times10^{-3})\,=\,0.77\times10^7$ m/s.

Sprite D continued to develop bidirectionally into frame c, extending up to about 80.0 km MSL altitude and down to about 63.7 km MSL in the right tendril branch (about 64.1 km MSL for the left). Sprite D's average upward development velocity in frame $c$ was therefore $0.40\times10^{7}$ m/s while its average downward velocity was $0.94\times10^{7}$ m/s. The average downward velocity estimate does not factor in the slight non-vertical motion of the tendril, the radial component of which can not be determined without triangulation.

The average downward velocity increased from frame $b$ to frame $c$ while the average upward velocity decreased by a factor of three. The increase and magnitude of the downward velocity is roughly consistent with the theoretical predictions of positive streamer velocities in sprites by Raizer et al. (1998) for a similar altitude extent.

In frame $d$, sprite D extended up to $\simeq\,$82.8 km MSL altitude while the right main branch of tendrils had extended below the field of view at $\lesssim\,$56.6 km MSL altitude. The average downward velocity for the right main branch of tendrils would have been $\gtrsim1.2\times10^{7}$ m/s. The average downward velocity for the left main branch of tendrils, which was still completely in the field of view, was $1.2\times10^{7}$ m/s. Thus, the right main branch of tendrils may have extended only slightly below the field of view. The average downward velocity in frame $d$ was greater than in frame $c$ and is the same as the maximum velocity of $1.2\times10^{7}$ m/s predicted by Raizer et al. (1998) for a similar total altitude extent.

Sprite B developed in a similar fashion as sprite D. Sprite B was first visible as three illuminated pixels in a vertical column in frame $b$. The altitude extent of this region was $\simeq\,$72.6-73.6 km, consistent with the $\simeq\,$72.9 km MSL origin of sprite D which was also determined on the assumption of a $\simeq\,$90 km MSL terminal altitude. In contrast, the altitude derived from the range to the +CG would have been 76.2-77.2 km MSL, at least 2 km lower than the sprite D origin of 79.3 km MSL based on the same range.

The upward developing component of sprite B reached $\simeq\,$81.8 km in frame $c$ with an average velocity of $2.0\times10^{7}$ m/s, significantly faster than the average initial upward velocity of sprite D in frame $b$. The downward-developing component of sprite B reached $\simeq\,$66.5 km MSL altitude on the left tendril branch in frame $c$ with an average downward velocity of $1.0\times10^{7}$ m/s. This velocity is comparable to the average downward velocity of sprite D ( $0.94\times10^{7}$ m/s) in the same frame, in spite of the delayed appearance by one frame of initial luminosity for sprite B relative to sprite D.

In frame $d$, the upper extent of sprite B was at $\simeq\,$83.4 km altitude while the lower extent was at $\simeq\,$59.3 km. The corresponding average velocities were $0.32\times10^{7}$ m/s and $1.2\times10^{7}$ m/s, respectively. The downward development velocity was essentially identical to that of sprite D in the same frame.

The pattern of development of the other sprites was similar to sprites B and D. All of the sprites appeared to develop bidirectionally from the first frame to the next. This development pattern is consistent with bidirectional streamer growth observed in laboratory experiments and predicted by theory (see Section 2.6.1).

The downward development velocites were similar for all of the sprites and did not exceed $1.2\times10^{7}$ m/s. The maximum velocity was consistent with the theoretical predictions of Raizer et al. (1998) for the maximum velocity of a downward-developing positive streamer under the influence of a 350 C$\cdot$km parent discharge. The downward developing tendrils also exhibited short persistence between adjacent frames. The short persistence will be explored in more detail in Section 5.2.5 for a sprite cluster with unusually bright tendrils.

The maximum upward average velocity of sprite bidirectional development was usually obtained in the second frame (the first possible frame for an average velocity measurement). These initial upward development velocities varied considerably from sprite to sprite, as was already demonstrated by intercomparing sprites B and D. The upward development velocity slowed down considerably after attaining an altitude of $\sim$81 km, which is consistent with the predicted altitude for the base of the ionosphere (Section 2.4.4). However, the continued advancement above this altitude is difficult to understand conceptually, particularly in light of the significant minimum electric field required to sustain negative streamer propagation (see Section 2.6.2).

The spatially-integrated luminosity of initial sprite development in frames $a$ and $b$ was below the detection threshold of the photometer (Figure 5.5). This demonstrates that a photometer may not give a reliable estimate of when sprites are initiated. This difficulty is further compounded by the fact that sprites within a sprite cluster often do not appear simultaneously. Rather, sprite appearance can be spread out over several milliseconds, as was the case here. Another (initially faint) sprite appeared in frame $e$ to the left of sprite A while two more sprites appeared in frame $f$, one just to the left of sprite B while the other was between sprites F and G. There may also have been additional sprites which formed behind the main cluster of sprites (B-F) after frame $d$.

The tendrils of sprites B, D, and F propagated downward out of the field of view in Figure 5.2e. A tendril segment above a branch point brightened significantly in frame $e$ on sprite D's right main tendril branch. The lower columnar portion of sprite B brightened and also bulged outward on the right side. This bulge probably was the beginning of an inferred negative streamer which propagated upward and to the right in frame $f$.

Additional tendril segments brightened in frame $f$. A striking feature is that the brightening occurred in the form of regularly spaced beads. Such beads were previously observed on tendrils by Mende et al. (1999). The tendril segments which brightened first on sprites B, D, and F were also the segments which propagated the furthest downward in frame $d$ relative to other segments associated with the same sprites (Figure 5.2d). A speculative possibility is that the lower altitudes (and faster propagation speeds) of the positive streamers were also associated with higher currents in the channels and this led to the subsequent brightening. However, it is not known how this could have produced a regular spacing of beads.

The development of sprite B through frames $e$-$j$ is shown in Figure 5.6. In this sequence, sprite B transitioned from a columniform sprite with tendrils to a carrot sprite, which is characterized by an upward-divergent ``V'' shape above downward-divergent tendrils. The sequence shows primarily the development on the left side of sprite B, since sprite C obscures much of the development on the right.

Figure 5.6: The formation of a V (carrot) shape for sprite B (see Figure 5.4). Inferred negative streamers are spawned from regions through which positive streamers propagated earlier. The upward-development of a couple of negative streamer groups for which average velocities (see text) were obtained are denoted with arrows.

In frame $f$ of Figure 5.6, an inferred negative streamer began its upward-propagation from the left tendril branch of sprite B. The arrow in frame $f$ denotes the streamer's tip location, which was at $\simeq$65.5 km MSL altitude. The streamer propagated up to $\simeq$69.9 km MSL (lower arrow) in frame $g$ at an average angle of $24^{\circ}$ from vertical. The corresponding average velocity of propagation was $0.97\times10^{7}$ m/s if there was no radial component. The average velocity would have been somewhat greater if there was a radial component. This streamer continued its upward propagation in frame $h$ at a reduced angle relative to vertical and had split several times. The uppermost tip is denoted by the lower arrow in frame $g$ at an altitude of $\simeq$76.8 km MSL. The corresponding average velocity of upward-propagation was $1.7\times10^{7}$ m/s, which was significantly greater than the average velocity in the previous frame.

The negative streamer continued its upward-development into frame $i$ to an altitude of $\simeq$84.2 km MSL (see arrow). The average streamer velocity of $1.8\times10^{7}$ m/s in frame $i$ was only slightly greater than in frame $h$. The width of the streamer increased noticeably in frame $i$ and this is even more pronounced in frame $j$. This expansion may be associated with penetration of the streamer into the ionosphere above $\simeq$81 km MSL. The streamer reached a terminal altitude of $\simeq$89.8 km MSL in frame $j$ with an average velocity which would have been greater than $1.3\times10^{7}$ m/s.

The inferred negative streamer which presumably originated within the column reached an altitude of $\simeq$75.0 km MSL (upper arrow) in frame $g$. The point of origin is difficult to determine due to the development of foreground tendrils from a sprite which originated in frame $f$ just to the left of sprite B. However, the point of origin is likely correlated with the bulge at $\simeq$70.7 km MSL. This bulge is opposite the origin of the inferred negative streamer which originated in frame $e$ and propagated to the right and upwards. The leftward streamer propagated up at an average angle of $35^{\circ}$ relative to vertical and an average velocity which would have been greater than $1.3\times10^{7}$ m/s. This streamer continued up to an altitude of $\simeq$80.9 km MSL (upper arrow) in frame $h$ at an average velocity of $1.4\times10^{7}$ m/s and terminated at a slightly higher altitude in frame i.

Numerous negative streamers initiated and developed in frames $e$-$m$ of Figures 5.2-5.3. The formation of negative streamers in each sprite was not simultaneous across the cluster, but was staggered in rough accordance with the different initiation times. The negative streamer velocities were similar to those reported above.