DNB H 0 *(n=3) Collisions with Plasma e - : Depopulating Rates for Low T e

1. 1010 109 108 107 106 Te = 50eV neK3 4 neK3 free (direct ionization) Total neK3 5 Rate (s-1) neK3 6-15 (Lorentz ionization for 50 keV beam in 5.4 T B-field. Levels up to n = 15 were included.) A3 1 A3 2 neK3 2 1012 1013 1014 1015 ne (cm-3) DNB H0*(n=3) Collisions with Plasma e-: Depopulating Rates for Low Te • Total transition rate  decay time  beam smearing length • Radiative decay dominates at low ne (below 1013 cm-3). Collisional processes (excitation, ionization) dominate at high ne (above 1014 cm-3). • Beam smearing for 50keV beam ranges from ~ 3 cm to ~1.5 mm

2. 1010 109 108 107 106 Te = 2000eV neK3 4 neK3 5 Rate (s-1) Total A3 1 neK3 free (direct ionization) A3 2 neK3 6-15 (Lorentz ionization for 50 keV beam in 5.4 T B-field. Almost exactly equal to direct ionization.) neK3 2 1012 1013 1014 1015 ne (cm-3) DNB H0*(n=3) Collisions with Plasma e-: Depopulating Rates for High Te • Similar to low Te case, but the higher Te reduces the effect of collisions. • Beam smearing for 50 keV beam ranges from ~ 3 cm to ~ 3 mm • 3 mm is a reasonable minimum limit for C-Mod, corresponding to Te ~ 2 keV and ne ~ 5 x 1014 cm-3 (typical of the most collisional C-Mod cores).

3. 1010 109 108 107 106 Rate (s-1) Levels 1-15 included 1012 1013 1014 1015 ne (cm-3) 50 keV DNB H0*(n=3) Collisions with Plasma H+: Depopulating Rates In Descending Order: Total neK3 4 (exc.) neCX3 3 (CX ion.) neK3 6-15 (Lorentz ion.) neK3 5 (exc.) neK3 2 (dec.) neK3 free (Direct ion.) neK3 1 (dec.) Applicable to Ti ~ 10 - 5000 eV. • Dominant collisional depopulating processes are ionization (especially via charge exchange) and excitation to n = 4.

4. 50 keV H0*(n=3) Collisions with e- and H+: Depopulating Rates for Low Te 1011 1010 109 108 107 106 Te = 10 eV • Electron collisional effects include excitation, decay, and ionization. • Proton collisional effects include excitation, decay, ionization, and charge exchange. Calculations were made assuming quasi-neutrality (ni = ne). • At low Te, the proton and electron effects are nearly equal. Total Depopulating Rate Rate (s-1) Total H0-e- Collisional Radiative Decay (A3 1 + A3 2) Total H0-H+ Collisional Levels 1-15 included 1012 1013 1014 1015 ne (cm-3)

5. 50 keV H0*(n=3) Collisions with e- and H+: Depopulating Rates for High Te 1011 1010 109 108 107 106 Te = 1000 eV • As Te increases, electron (and therefore total) collisional effects decrease. • Proton collisional effects are fairly insensitive to Ti as long as Ti < EH0. This holds for C-Mod, where Ti (~ Te) peaks at 1-5 keV (compared to DNB of 50 keV). Total Depopulating Rate Rate (s-1) Total H0-e- Collisional Radiative Decay (A3 1 + A3 2) Total H0-H+ Collisional Levels 1-15 included 1012 1013 1014 1015 ne (cm-3)

6. Smearing lengths of emission (from n=3) for a 50 keV beam 10 1 0.1 0.01 • Strong dependence on ne. Weak dependence on Te. • Does not include impurity collisions. • Does not include the characteristic lifetime of the limiting populating transition (2 3). Lb (cm) Te = 1000 eV Te = 10 eV 1012 1013 1014 1015 ne (cm-3)

7. Smearing lengths of emission (from n = 3 and n = 2) for a 50 keV beam 10 1 0.1 0.01 • Smearing of n = 2 state is ~ 4 mm at 1014 , while that of n = 3 state is ~ 3 mm. Lb (cm) n = 2 n = 3 1012 1013 1014 1015 ne (cm-3)

8. 50 keV DNB H0*(n=3) Collisions with Plasma Impurities Aq+: Depopulating Rates 1010 109 108 107 106 Total neCX3 3 (CX + Ion.) neK3 4 (exc.) neK3 6-15 (Lorentz ion.) neK3 5 (exc.) neK3 2 (dec.) neK3 1 (dec.) • As with the proton processes, the dominant impurity processes are ionization and excitation to n = 4. Summed over q 1-8. Rate (s-1) Levels 1-15 included 108 109 1010 1011 1012 1013 nz (cm-3)

9. 50 keV DNB H0*(n=3) Collisions with Plasma Impurities Aq+: Depopulating Rates 1011 1010 109 108 107 • For 10% impurities (nz = 0.1 ne), ions with charge states 2+ to 6+ will all make a significant impact on the depopulation rate (increasing it by 15 to 100%). • For 1% impurities (nz = 0.1 ne), the 2+ to 6+ states do not make a significant impact. Q = 6 Q = 5 Q = 4 Q = 3 Q = 2 Q = 1 Rate (s-1) Total rate for e- and p+ collisions for ni ~ ne = 100 nz (1% impurities) Total rate for e- and p+ collisions for ni ~ ne = 10 nz (10% impurities) 1010 1011 1012 1013 1014 nz (cm-3)

10. 50 keV DNB H0*(n=3) Collisions, including Impurities (Aq+): Depopulating Rates 1011 1010 109 108 107 106 Te = 200 eV • The selected Zeff were used to determine the relative density of A5+. For instance, Zeff of 1.5 can be achieved with a 2.5% density of B5+. • As Zeff increases, impurity (and therefore total) collisional effects increase. Total Rate for various Zeff (1, 1.5, 2, 3, 5) Total H0-e- and H0-H+ Collisional Rate (s-1) Radiative Decay (A3 1 + A3 2) H0-A5+ Collisional for various Zeff (1.5, 2, 3, 5) 1012 1013 1014 1015 ne (cm-3)

11. Smearing lengths of emission for a 50 keV beam 10 1 0.1 0.01 • Zeff = 5 can reduce smearing significantly (by a factor of 2X for plasma densities above 1013 cm-3). • This may be one of the mitigating factors in the plasma edge. Lb (cm) Zeff = 1 Zeff = 5 1012 1013 1014 1015 ne (cm-3)

12. DNB H0*(n=3) Collisions with Plasma H+: CX and Direct Ionization 10-5 10-6 10-7 • CX dominates at these low-to-mid E’s. Rolls off relative to K at higher E’s (Beam Pen). • Two refs. roughly agree for total ionization, though only within a factor of ~2 at 20 keV. • Elementary procs. gets CX (to 20 keV) from Smirnov. K (to high E) from BEA [ref??]. • Beam Pen. gets total X-section from classical theory (Janev, ‘83). CXp3 3 + Kp3 free (Total Ionization. From Elementary Processes..., Janev ‘87.) CXp3 3 (Resonant charge-exchange with a proton. From Elementary Processes..., Janev ‘87.) <v> (cm3/s) CXp3 3 + Kp3 free (Total IonizationFrom Beam Penetration..., Nuclear Fusion, Janev ‘89.) Kp3 free (Direct ionization by proton. From Elementary Processes..., Janev ‘87.) 5 10 15 20 Ebeam (keV)