Validating modelling assumptions of alpha particles in electrostatic turbulence

To rigorously model fast ions in fusion plasmas, a non-Maxwellian equilibrium distribution must be used. In the work, the response of high-energy alpha particles to electrostatic turbulence has been analyzed for several different tokamak parameters. Our results are consistent with known scalings and experimental evidence that alpha particles are generally well-confined: on the order of several seconds. It is also confirmed that the effect of alphas on the turbulence is negligible at realistically low concentrations, consistent with linear theory. It is demonstrated that the usual practice of using a high-temperature Maxwellian gives incorrect estimates for the radial alpha particle flux, and a method of correcting it is provided. Furthermore, we see that the timescales associated with collisions and transport compete at moderate energies, calling into question the assumption that alpha particles remain confined to a flux surface that is used in the derivation of the slowing-down distribution.Comment: 23 pages, 13 figures, submitted to the Journal of Plasma Physic

William Wilkie to John Kean, September 23, 1790

William wrote to John, addressed to New York via Captain Elliott. William says Merchants won\u27t agree on a price for indigo, so sales were slow since January. He sent a pair of shoes for enslaved people for a pattern (not included). Name included: Mr. Barnwell.https://digitalcommons.kean.edu/lhc_1790s/1066/thumbnail.jp

William Wilkie to John Kean, July 24, 1790

William wrote to John, addressed to New York. He enclosed an account sale for John\u27s indigo and a statement of John\u27s bond to Thomas Agier (neither are attached). William also sent 8 packets of newspapers by Captain Elliot. He wrote about South Carolina Medium [money] and its value. Names included: Mr. Chisholm, Mr. Holmes, Maxwell, and Mr. White.https://digitalcommons.kean.edu/lhc_1790s/1061/thumbnail.jp

William Wilkie to John Kean, April 14, 1790

William Wilkie, from Charleston, wrote to John Kean, addressed to New York via Captain Snell. John\u27s indigo and rice are not selling. Nothing will sell for near its value and when sold, Vendue [auction] Masters find it difficult to collect the money. Names included: Oliver Stackweather (will deliver newspapers to John), Mr. White, and Mr. Pringle.https://digitalcommons.kean.edu/lhc_1790s/1053/thumbnail.jp

William Wilkie to John Kean, September 22, 1789

William Wilkie wrote from Charleston to John Kean addressed to Beaufort, SC. He had written to John by Dr. Campbell and received his letter from Captain Saltus, but Saltus left before he finished his reply so he sent it by Mr. D. Adams of St. Helena instead. He was working on selling the rice and had received 2o pounds for him from Mr. Elliott. He had not yet found a purchaser for Sancho, an enslaved man, and planned to sell him and the horses at auction with John\u27s approval.https://digitalcommons.kean.edu/lhc_1780s/1310/thumbnail.jp

William Wilkie to John Kean, November 19, 1789

William Wilkie wrote from Charleston to John Kean, addressed to New York, NY. He had not heard from John since he wrote by Captain Elliott. He was enclosing a second copy of the Bill of Exchange from William Crafts and Murray, Mumford, & Bowen, Merchants to make sure John had it. He received a shipment for John containing ravens, ducks, thread, and osanbrigs (a type of cheap, course linen usually used to make clothing for enslaved people). He wrote he would follow John\u27s instructions for this shipment and that he sent the rest of it to him in New York. He also mentioned that the price of rice was not yet fixed.https://digitalcommons.kean.edu/lhc_1780s/1318/thumbnail.jp

William Wilkie to John Kean, October 27, 1789

William Wilkie wrote from Charleston to John Kean, addressed to New York, NY. He received John\u27s letter along with a check sent from William Stephens that was previously sold by John Grive. He enclosed a bill for $150 from Mr. Crafts, Murray, Mumford, and Bowen as well as a current statement of account. Captain Blake would like a bill of sale for the enslaved man he bought from John. This is most likely a man named Sancho that had been mentioned in previous letters. He received several items from the Britannia and sent them to Beaufort.https://digitalcommons.kean.edu/lhc_1780s/1317/thumbnail.jp

William Wilkie to John Kean, December 25, 1789

William Wilkie wrote from Charleston to John Kean, addressed to New York, NY. John did not mention the certification of exchange from William Craft and Murray, Mumford, and Bowen, so he enclosed another copy of it. By John Wood he was sending rice for the balance that was due to John. He had yet to sell the duck, osnabrig, and thread. He sold some of Stoney\u27s indigo, paid Alexander Chisolm, and forwarded Robert Barnwell\u27s letter.https://digitalcommons.kean.edu/lhc_1780s/1324/thumbnail.jp

William Wilkie to John Kean, September 18, 1789

William Wilkie wrote from Charleston to John Kean, addressed to Beaufort, SC. Since his last letter sent via Dr. Campbell, he heard back from Captain Tucker who declined to take the Keans to New York. He asked Captain Keen, but would not have an answer until Monday. He suspected he would decline as he was involved with trade between charleston and Georgetown. He received the order addressed to Mr. Chisolm, however, the man who it was from\u27s rice had not sold and the order could not be paid until it was. He would write again by Mr. Elliott after he heard from Keen.https://digitalcommons.kean.edu/lhc_1780s/1305/thumbnail.jp

William Wilkie to John Kean, April 11, 1789

William Wilkie wrote from Charleston to John Kean, addressed to Beaufort, SC. He wrote regarding the sale of some indentures John had. Indentures were not selling for much, but he was trying to find a good deal. He also wrote regarding various ships going to and from New York and Philadelphia, as well as who was traveling on them. People Included: Alexander Chisolm, Mr. Calcoch, Mr. Tunno, Captain Strong, Captain Eliott, Captain Snell, Mr. Steward, Pierce Butler, Ralph Izard, Captain B. Tucker, Captain Sattus, and Carmand & Tinker.https://digitalcommons.kean.edu/lhc_1780s/1265/thumbnail.jp