P10 Properties (Calculated)

The tables below were calculated by Roy Bossingham using Magboltz 2, V3.1 (Biagi, 2000) for typical values of interest to STAR: T=23.9C, P=760 Torr and B=5.0, 2.5 and 0.0 kG, with additional values to help with interpolation. E values were most concentrated around E=148 V/cm, and were parallel to B in all cases.

The drift velocity and diffusion constant are functions of the ratio of E over density; to find the drift velocity and single-electron diffusion at fixed B, general values of the drift length L and small changes from the input values of (cm)E (V/cm), P (Torr) and T (K):

• Use (E/P) * (T / 297.04 K) for the "E/P" column.

• Look up the appropriate value (note that, for parallel E and B in Magboltz, Sigma_T is a function of B, but drift velocity and Sigma_L are not).

• Scale Sigma_L and Sigma_T by sqrt[L * (760 Torr / P) * (T / 297.04 K)] to get the diffusion in um.

Magboltz 2 uses Monte Carlo methods, with the statistics determined by the collisions parameter. Statistics were used corresponding to collisions=120, or higher, giving a precision of at least 0.04% in drift velocity and 1.6% in diffusion.

Drift velocity in P10 vs E for P=760 Torr and E parallel to B, from a rather global viewpoint.
The STAR TPC normally operates just beyond the peak in the right-hand plot.

Diffusion in P10 vs E for P=760 Torr and E parallel to B.

Drift velocity and longitudinal diffusion in P10 vs E for P=760 Torr and E parallel to B.
The plotted parameters are close to the operating conditions for the STAR TPC drift volume.

Transverse diffusion in P10 vs E for P=760 Torr and E parallel to B. The plotted
parameters are close to the operating conditions for the STAR TPC drift volume.

Blum and Rolandi define the variable D, which is proportional to the transverse diffusion squared and a function of E and B; they plot it for the special case of P9 (relevant to Aleph) and E=110 V/cm. D(0)/D(B) becomes a straight line at sufficiently high B (higher than in STAR, however). As the lefthand plot below shows, D(0)/D(B) varies smoothly and slowly with B^2 and E, making it useful for interpolation. However, as the righthand plot shows, Blum and Rolandi's P9 plot does not apply especially well to STAR's operating conditions.

Transverse diffusion in P10 vs E for P=760 Torr and E parallel to B. The plotted
parameters are close to the operating conditions for the STAR TPC drift volume.

 E (V/cm) E/P (V/cm-Torr) V (cm/us) Sigma_L (um/sqrt(cm)) 50 0.0658 3.427 618 75 0.0987 4.628 499 100 0.1316 5.239 427 118 0.1553 5.434 395 128 0.1684 5.473 377 138 0.1816 5.487 363 148 0.1947 5.472 356 158 0.2079 5.453 341 168 0.2211 5.397 342 178 0.2342 5.345 331 188 0.2474 5.281 325 200 0.2632 5.189 323 250 0.3289 4.802 298 375 0.4934 3.968 261 500 0.6579 3.410 239 750 0.9868 2.839 222 1000 1.3158 2.573 219 1500 1.9737 2.380 219 2000 2.6316 2.340 218 3000 3.9474 2.360 211 4000 5.2632 2.410 217 6000 7.8947 2.828 246 8000 10.5263 3.385 243 12000 15.7895 4.552 219 16000 21.0526 5.631 201 24000 31.5789 7.713 172 32000 42.1053 9.699 157

Calculated drift velocity [cm/us] and longitudinal diffusion [um/sqrt(cm)] in P10 for parallel
E and B at P=760 Torr and T=23.9C  . Values are nearly independent of the magnitude of B.

 B (kG) E (V/cm) E/P (V/cm-Torr) 5.0 4.375 3.75 3.125 2.5 1.875 1.25 0.625 0.0 50 0.0658 162 268 592 75 0.0987 168 282 583 100 0.1316 191 296 569 118 0.1553 209 314 562 128 0.1684 218 240 258 290 322 377 446 529 560 138 0.1816 227 267 337 452 571 148 0.1947 240 253 277 306 346 390 463 531 575 158 0.2079 250 287 352 468 554 168 0.2211 255 276 299 324 351 416 469 542 566 178 0.2342 260 302 371 494 577 188 0.2474 270 314 379 487 575 200 0.2632 289 392 571 250 0.3289 325 433 580 375 0.4934 396 486 589 500 0.6579 460 534 610 750 0.9868 514 574 620 1000 1.3158 533 583 592 1500 1.9737 537 566 580 2000 2.6316 541 550 561 3000 3.9474 503 4000 5.2632 478 498 498 6000 7.8947 432 8000 10.5263 385 386 388 12000 15.7895 317 16000 21.0526 282 280 284 24000 31.5789 231 32000 42.1053 201 203 203

Transverse diffusion [um/sqrt(cm)] in P10 (calculated)
for parallel E and B at P=760 Torr and T=23.9C  .

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