# Presentation: 540486

## Systems Code Results: Impact of Physics and Engineering Assumptions

**J. F. Lyon,  ORNL**
**ARIES Meeting        Sept. 15, 2005**

**Notes:**
The design is being done as a collaboration

## Topics

**Optimization Approach**
**Plasma and Coil Treatment**
**Systems Optimization Code**
**NCSX reference case results**
**Parameter scans and variations**
**Next steps**

## Approaches Used to Define Reactor Parameters

**1-D systems cost optimization code**
- calculates self-consistent plasma and component parameters
- minimizes cost of electricity
**1-D power balance determines plasma parameters and path to ignition**
- incorporates density and temperature profiles; overall power balance; radiation, conduction, alpha-particle losses
**0-D scoping study determines device parameters**
- calculates <*R*axis>, <*B*axis>, <**>, <*p*n,wall>, *B*max, *j*coil, etc. subject to limits and constraints
**Sensitivity to models, assumptions & constraints examined at each stage**

## Parameter Optimization Integrates Plasma/Coil Geometry and Reactor Constraints

-   Shape of last closed flux surface
-    and <*R*axis>/<*a*plasma>, ** limit
-   Shape of modular coils and
*   **B*max,coil/*B*axis vs coil cross section,
-    <*R*coil>/<*R*axis>,  min/<*R*axis>
-   Alpha-particle loss fraction

-   Blanket and shield thickness
-   *B*max,coil vs *j*coil for superconductor
-   Acceptable wall power loading
-   Access for assembly/disassembly
-   Component costs/volume

-   <*R*axis>, <*a*plasma>, <*B*axis>
-   *B*max,coil, coil cross section, gaps
-   *n*e,I,Z(r),*T*e,i(r), <**>, *P*fusion, *P*rad, etc.
-  Operating point, path to ignition
-  Cost of components, operating
-    cost       cost of electricity

## Reactor Core (Plasma and Coil) and Operating Point Optimizations are Separate 

**Reactor core optimization leads to a *****fixed***** plasma and coil geometry**
** ****integrated 3-D plasma/coil optimization code**
**  ****plasma shape, aspect ratio, coil geometry**
**  ******** ****limits, helical ripple, edge geometry**
**  ****plasma-coil and coil-coil spacings, etc.**
**Operating point optimization leads to plasma parameters, profiles, field and component sizes**
**1-D systems code incorporating complex plasma and coil geometry and stellarator physics modules**

## Minimum  Reactor  Size  Is  Determined  by  

- <date/time>

**Minimum  Reactor  Size  Is  Determined  by  ******

**A configuration is character-ized by the ratios *****A********* = *****R*****0****/********,         *****A*****p**** = *****R*****0****/<*****a*****>, and *****B*****max****/*****B*****0**
**The minimum reactor size is set by *****R*****0**** = *****A*********(D + ct/2) where D is the space needed  for scrapeoff, first wall, blanket, shield, coil case, and assembly gaps**
**Cost******** surface area ******** *****A*********2****/*****A*****p**

## Several Plasma and Coil Configurations Have Been Studied

## Bmax/Baxis Depends on Coil Cross Section

**Larger plasma-coil spacings lead to more convoluted coils and higher *****B*****max****/<*****B*****axis****>**
**Minimum coil-coil separation distance determines *****k*****max**

## NCSX Configurations Permit a No-Blanket Region

**Plasma-coil separation is small only over 5% of the wall area**
**A transition region with tapered blanket and shield covers 10% of the wall area**
**The full blanket covers 85% of the wall area**
**Not possible with MHH2 configurations because coils are same distance from plasma everywhere**

## Conductor j and Cost Varies with Bmax

**Conductor cost =****    const *****B*****axis****<*****R*****>****2****[f(*****B*****max****)]**** **
**Cost of winding coil =**** conductor mass x $80/kg ****	****const *****B*****axis****<*****R*****>****2 ****/*****j*****(*****B*****max****)**
**Coil structure =**** volume x 7800 kg/m****3**** x $56/kg = k****3****<*****R*****>****2**

## Studied Port Maintenance Approach

**Three #1 and six #2 ports possible**

## Parameters Depend on Neutron Wall Power

**0-D NCSX values are determined by *****p*****n,max**** = 5 MW/m****2**
**<*****R*****> = 6.2 m, <*****B*****axis****> = 6.5 T, *****B*****max**** = 12.7 T**

## 0-D Scaling of Main Reactor Parameters

**Maximize <*****p*****wall****> subject to *****j*****SC****(*****B*****max****) and radial build constraints**
**blanket, shield, structure, vacuum vessel ~ wall area ~ 1/<*****p*****n,wall****>**
**volume of coils ~ L****coil****I****coil****/*****j*****coil**** ~ <*****R*****>****1.2**** ~ 1/<*****p*****n,wall****>****0.6**
**blanket replacement and other costs independent of <*****p*****n,wall****>**
**Fix maximum neutron wall loading *****p*****n,wall**** at 5 MW/m****2**
**peaking factor = 1.52          <*****p*****n,wall****> = 3.3 MW/m****2****  **
**<*****p*****wall****> = 3.3 MW/m****2     ****       wall area = 480 m****2**** for *****P*****fusion**** = 2 GW**
-  **<*****R*****> = 6.2 m for NCSX vs. <*****R*****> = 14 m for SPPS**
**Chose <**********> = 6%: **no reliable instability ** limit, high equilibrium limit
* ***<*****B*****axis****> = 5.8 T for NCSX**
***B*****max**** on coil depends on plasma-coil spacing & coil cross section**

##  Systems Optimization Code

**Minimizes ****Cost of Electricity**** for a given plasma and coil geometry using a nonlinear constrained optimizer**
**Iterates on a number of optimization variables**
_**plasma**_**: <*****T*****i****>, <*****n*****e****>, conf. multiplier;  **_**coils**_**: width/depth of coils**
_**reactor variables**_**: <*****B*****axis****>, <*****R*****>**
**Large number of constraints allowed (=, <, or >)**
***P*****electric****, ********** limit, confinement multiplier, coil***** j***** and *****B*****max****, clearance radially and between coils, TBR, neutron wall power density **
**Large number of fixed parameters for **
**plasma and coil configuration, plasma profiles,**
**transport model, helium accumulation and impurity levels,**
**SC coil model (*****j*****,*****B*****max****), blanket/shield concepts, and**
**engineering parameters, cost component algorithms**

## Optimization Approach

**Iterates on a large number of variables**
_**plasma:**_** T****e****(r), T****i****(r), n****e****(r), n****e****(r), **********, Z****eff****, H-ISS95, power components (coronal and bremsstrahlung radiation, ********i, ********e), ******** losses, etc.**
_**coils**_**: max. & min. width/depth of coils, clearance between coils, components volumes and costs, *****j*****, *****B*****max****, forces**
_**reactor variables**_**: *****B*****0****, <*****R*****>, blanket volumes, TBR, neutron wall loading, *****P*****electric****, divertor area, access between coils, radial build, etc.**
_**costs**_**: equipment cost, annual operating cost, total project cost, CoE**

## MHHOPTNEW Reactor Optimization Code

_**input**_**:**** ****physics, coil, costing, geometry, reactor component**
**parameters and**
**constraints**

_**plasma/**__**profile**__** solver**_
***T*****e****(r)****, *****T*****i****(r)****, *****n*****e****(r)****, *****n*****i****(r)****,**
***n*****Z****(r), ****E****r****(r),**** **********, Z****eff****, *****P*****rad****, *****P*****fusion****, *****P*********,loss****, *****P*****wall****, **_***P***__**divertor**_**,**** **********E****, etc.**

_**usual constraints**_
***P*****electric**** = 1 GW**
**ignited plasma**
**max. confinement mult.**
**max. <**********>, max. density**
**radial build & port width**
**max. *****B*****max**** on coil**
**max. <*****p*****n,wall****>**

**existing parts     **_**will update**_**     ****no plans to use**

## Component and Cost Models

**Geometry factors for blankets, shields, vacuum**
**     ****vessel and coils from L-P Ku**
** ****Blanket/shield models from L. ElGuebaly**
**3 blanket/shield areas (with fractions)**
**<*****p*****wall****> limit and shield thickness**
** ****Updated ARIES costing algorithms**
**2004 costs for blanket/shield/vacuum vessel from L. Waganer and for coils from L. Bromberg**
**inflation factor from 1980 for other costs**
** ****Compare results against 0-D optimization and 1-D POPCON calculations**

## Determination of Plasma Parameters

**Too many variables, need to make some assumptions**
**choose H-ISS95 < 6 **
**assuming improvements due to quasi-symmetry and experience**
**choose impurity levels: 0.5% C and 0.005% Fe**
**20% alpha-particle losses (better cases have been developed)**
**choose **********He*****/**********E**** = 6**
**Choose profile shapes**
**choose hollow *****n*****e****(r) with center/peak = 0.8**
**choose *****T***** ~ parabolic****1.5**
- need better transport model (, *E*r) to determine self-consistent *T*e(r),*T*i(r)
-  full 1-D model with self-consistent *E*r is in the systems code
**Test sensitivity to these assumptions **

## Treatment of Impurities

** *****n*****e**** = *****n*****DT**** + ********Z*****n*****Z****, so impurities reduce *****P*****fusion**** through**
**reduced *****n*****DT****2**** and **********2**** (~ *****n*****e**** + *****n*****DT****)****2****; *****P*****fusion**** ~ *****n*****DT****2**** ~**********2****B****4**
**reduced *****T*****e**** (hence *****T*****i****) through radiative power loss**
**requires higher *****B***** or H-ISS95 or larger *****R***** to compensate**
** ****carbon (Z****C**** = 6) for low Z & iron (Z****Fe**** = 26) for high Z**

**Standard corona model:**** ****line radiation and electron-ion recombination**
***p*****radiation**** ~ *****n*****e*****n*****Z ****f(*****T*****e****)**

## Power Flows

## Typical Systems Code Summary

**NCSX case (NKZD)**
**modified LiPb/FS/He H2O-cooled **
**internal vacuum vessel with SiC inserts**
**and tapered blanket,  port maintenance**
**inflation factor                             2004 year**
**following CONSTRAINTS were selected:**
**ignition = 1 target                           1.00**
**Electric Power (GW)                       1.00**
**volume averaged beta                    0.05**
**sufficient radial build**
**maximum neutron wall load          5.00**
**maximum  jcoil/jSC(Bmax)             1.00**
**maximum density = 2 x nSudo**
**max. confinement multiplier           6.0**
**minimum port width****	****                      2.0**
**VARIABLES  selected for iteration**
**major radius                     5.00          16.00**
**field on axis                      3.00          10.00**
**ion density                        1.00          10.00**
**ion temperature                1.00          20.00**
**coil radial depth                0.03           1.00**
**confinement multiplier    0.10            9.00**

**  **

**FIGURE OF MERIT .....................**
**  ****66.9      Cost of Electricity**
**FINAL VALUES OF CONSTRAINTS:**
**ignition margin                                   1.00**
**Electric Power (GW)                           1.00**
**volume averaged beta (%)                 5.00**
**radial build margin                             1.00**
**max. neutron wall load (MW/m****2****)       5.00**
**jcoil/jSC(Bmax)                                   1.00**
**average/maximum density                0.93**
**ratio of tauE to conf. multiplier         4.23**
**maintenance port width (m)****	****      2.28**
**FINAL DESIGN**
**major radius (m)                                6.73**
**field on axis (T)                                  6.19**
**max. field on coil (T)                        14.03**
**volume avg. density (10****20**** m****–3****)        4.03**
**density averaged temp (keV)            6.08**
**coil dimensions (m x m)              0.18 x 0.65**
**current density (MA/m****2****)                   107**

## Typical Systems Code Summary

**Plasma Parameters**
**central ion temp (keV)                      9.15**
**central ion density (10****20**** m****–3****)          8.59**
**central elec. density (10****20**** m****–3****)        9.11**
**fraction fuel to electrons                  0.91**
**confinement time, taue (sec)           0.95**
**stored plasma energy (MJ)               343**
**volume averaged beta (%)               5.00**
**beta star (%)                                      8.21**
**fraction carbon impurity                    0.5 %**
**fraction iron impurity                       0.005 %**
**fraction helium                                  3.11 %**
**Z effective                                          1.25**
**Mass Summary**
**total nuclear island (tonnes)          5,078**
**mass LiPb coolant (tonnes)           3,264**
**total mass (tonnes)      ****	****         8,342**

**  **

**Power Balance**
**net electric power (MW)               1000**
**gross electric power (MW)        1054.9**
**fusion power (MW)                     2258.5**
**thermal power (MW)                   2511.6**
****** ****heating power (MW)                 450.9**
**power in neutrons  (MW)           1807.6**
**radiated power   (MW)                  349.5**
**fuel bremsstrahlung  (MW)          238.1**
**carbon radiation  (MW)                  53.0**
**iron radiation (MW)                        57.4**
**synchrotron radiation (MW)            1.0**
**conduction power   (MW)              11.2**
**fusion power to plasma  (MW)    360.7**
**fraction alpha power  lost             20.0 %**
**radiated power fraction                 77.5 %**
**ave neut wall load (MW/m****2****)            3.29**
**ave rad wall load (MW/m****2****)              0.64**

## EISS-95 = 0.26Pheating–0.59<ne>0.51<Baxis>0.83<R>0.65<a>2.212/30.4

**NCSX: ********E****/********E****ISS-95**** = 4.2,  <*****T*****> = 9.5 keV, <*****n*****> = 3.5 10****20**** m****–3****, <**********> = 6.1%**

********E****ISS-95**** = 0.26*****P*****heating****–0.59****<*****n*****e****>****0.51****<*****B*****axis****>****0.83****<*****R*****>****0.65****<*****a*****>****2.21**********2/3****0.4**

**H-ISS95 =**
********E****/**********E****ISS-95**

## Operating  Point  Moves  to  Higher  <T> with Lower Pstartup as  ISS95  Multiplier  H  Increases

**Operating  Point  Moves  to  Higher  <*****T*****> with Lower P****startup**** as  ISS95  Multiplier  H  Increases**

**Example:*****  R***** = 9 m, *****B***** = 5 T, 5% ******** losses, ********He****/********E**** = 6**

**H = 2**

**H = 2.15**

**H = 2.5**

**H = 3**

**<T> (keV)**

**<n> (10****20**** m****–3****)**

**x**

## Component Cost Summary (2004$)

**total mod coil + str cost        138.2**
-     mod coil SC cost                   69.0
-     rest mod coil pack cost         15.8
-     coil structure cost                  53.4
- total VF coil cost                         0.0
- divertor coil cost                          0.0
- total coil cost                           138.2
- bucking cylinder cost                  0.0
**total blanket, first/back wall      56.4**
-     first wall cost                             5.8
-     front full blanket cost               24.5
-     front blanket back wall cost     24.5
-     second blanket cost                  0.0
-     transition blanket cost               1.6
**total vacuum vessel cost            49.9**
-     full blanket vac vessel cost        43.1
-     shield-only vac vessel cost          2.1
-     transition vac vessel cost             4.8

**shield cost and back wall             97.9**
-     ferritic steel shield cost                33.6
-     1st shield-only WC shield cost      2.6
-     shield-only back wall cost            20.5
-     2nd shield-only WC shield cost     6.4
-     1st transition WC shield cost         2.2
-     trans shield back wall cost           22.7
-     2nd transition WC shield cost      10.1
**cost of manifolds                         147.5**
-     full manifold cost                          99.5
-     transition manifold cost                48.0
**cost of liquid metal coolant         166.5**

## Values for Different Coil Configurations

**ISS-95 confinement improvement factor of 3.2 to 4.4 is required; present stellarator experiments have up to 2.5**
**ISS-2004 scaling indicates ********eff****–0.4**** improvement, so compact stellarators with very low ********eff**** should have high H-ISS values**

## Values for Different pwall Limits

## Cost Varies as 1/<pn,wall>

**set by**
**radial**
**constraint**

## Weak Variation of Reactor Parameters with 

**Increasing <**********> allows reduced <*****B*****axis****>, *****B*****max**** and <*****R*****>**

## Weak Variation of COE with and A

## Variation of Reactor Parameters with 

**Increasing <**********> allows reduced <*****B*****axis****> and <*****R*****> (until p****wall**** limit) but requires larger H-ISS9****5**

## Variation of Coil Parameters with 

## Parameters Insensitive to Profile Assumptions

## Larger H-ISS95 is Required to Offset Higher Alpha-Particle Losses

## Next Steps

**Incorporate ********* as target**
**neoclassical impurity profiles**
**1-D calculation of T****e****(r) & T****i****(r)**
**NbTi(Ta) coils**
**Field period maintenance approach**

## Further Modeling of Impurities Is Possible

**Present approach **
**assumes *****n*****C**** = f****C*****n*****e**** & *****n*****Fe**** = f****Fe*****n*****e****;  f****Z**** = constant thruout plasma, so *****n*****Z****(r) has same (slightly hollow) profile as *****n*****e****(r)**
**Use neoclassical model for impurity profiles**
***n*****Z****(r) = *****n*****e****(r) x <f****Z****> (*****n*****e****/*****n*****e0****)****Z**** ****[*****T*****e****/*****T*****e0****]****–Z/5**
** ****conservative approach:**** ignore [*****T*****e****/*****T*****e0****]****–Z/5**** term because it probably is not applicable in stellarators**
** *****n*****Z****(r) more peaked near edge since *****n*****e****(r) is hollow for regime of interest**
** *****n*****Z****(r) peaked at center if *****n*****e****(r) peaked**

## Impurity Density Profiles

**C**

**Fe**

## Full 1-D Transport Matrix Calculations are in Systems Code

**Example case: *****R*****0**** = 12 m, *****a*****p**** = 1.5 m, **
***    ******B*****0**** = 7 T, *****P*****fus**** = 3 GW (thermal),**
**    ****edge helical field ripple ********h****(*****r***** = *****a*****p****) = 0.1**

## Field Period Maintenance Approach

## Summary

**Parameter determination integrates plasma & coil geometry with physics & engineering constraints and assumptions **
**Results lead to factor ~2 smaller stellarator reactors (<*****R*****> = 7–8 m), closer to tokamaks in size**
**Examined 6 different plasma/coil configurations and two blanket/shield concepts**
**CoE is relatively insensitive to assumptions (**********, f********,loss****) for a plasma/coil configuration; variation is in H-ISS95**
**Further steps: incorporate ********* as target, 1-D calculation of T****e****(r) & T****i****(r), NbTiTa coils, field period maintenance approach**