Tokamak GOLEM Basic diagnostics

Procedure (This notebook to download)

bash wrapper, Error log

Prerequisities: function definitions

Load libraries

%matplotlib inline
import os
import numpy as np
import matplotlib.pyplot as plt
from scipy import constants, integrate, signal, interpolate
import sqlalchemy   # high-level library for SQL in Python
import pandas as pd
import subprocess

For interactive web figures

import holoviews as hv
hv.extension('bokeh')
import hvplot.pandas

For conditional rich-text boxes

from IPython.display import Markdown

Define global constants.

data_URL = "http://golem.fjfi.cvut.cz/shots/{shot_no}/Diagnostics/PlasmaDetection/{identifier}"  # TODO workaround
parameters_URL = 'http://golem.fjfi.cvut.cz/shots/{shot_no}/Production/Parameters/{identifier}'

destination='Results/'
#os.makedirs(destination, exist_ok=True );
# try to get thot number form SHOT_NO envirnoment variable, otherwise use the specified one
shot_no = os.environ.get('SHOT_NO', 0)

The DataSource downloads and caches data (by full URL) in a temporary directory and makes them accessible as files.

ds = np.DataSource(destpath='/tmp')

def print_and_save(phys_quant, value, format_str='%.3f'):
    print(phys_quant+" = %.5f" % value)
    with open(destination+phys_quant, 'w') as f:
        f.write(format_str % value)
    update_db_current_shot(phys_quant,value)    
        
def update_db_current_shot(field_name, value):
    # subprocess.call(["export PGPASSWORD=`cat /golem/production/psql_password`;psql -q -U golem golem_database --command='UPDATE operation.discharges SET \""+field_name+"\"="+str(value)+" WHERE shot_no IN(SELECT max(shot_no) FROM operation.discharges)'"],shell=True)
    subprocess.call(["export PGPASSWORD=`cat /golem/production/psql_password`;psql -q -U golem golem_database --command='UPDATE diagnostics.basicdiagnostics SET \""+field_name+"\"="+str(value)+" WHERE shot_no IN(SELECT max(shot_no) FROM diagnostics.basicdiagnostics)'"],shell=True)
    
    
def open_remote(shot_no, identifier, url_template=data_URL):
    return ds.open(url_template.format(shot_no=shot_no, identifier=identifier))

def read_value(shot_no, identifier):
    """Return the value for given shot as a number if possible"""
    value = open_remote(shot_no, identifier, data_URL).read()
    return pd.to_numeric(value, errors='ignore')

def read_parameter(shot_no, identifier):
    return open_remote(shot_no, identifier, parameters_URL).read().strip()
    
def read_signal(shot_no, identifier): 
    file = open_remote(shot_no, identifier, data_URL + '.csv')
    return pd.read_csv(file, names=['Time',identifier],
                     index_col='Time', squeeze=True)  # squeeze makes simple 1-column signals a Series

def correct_inf(signal):
    """Inteprolate Inf values"""
    signal = signal.replace([-np.inf, np.inf], np.nan).interpolate()
    return signal

t_Bt = float(read_parameter(shot_no, 'TBt')) * 1e-6  # from us to s
t_CD = float(read_parameter(shot_no, 'Tcd')) * 1e-6  # from us to s
offset_sl = slice(None, min(t_Bt, t_CD) - 1e-4)

Plasma detection result loading

This part of the algorithm is done with higher priority before the this notebook

b_plasma = read_value(shot_no, destination+'b_plasma') == 1
t_plasma_start = read_value(shot_no, destination+'t_plasma_start')
t_plasma_end = read_value(shot_no, destination+'t_plasma_end')
plasma_lifetime = read_value(shot_no, destination+'t_plasma_duration')
if b_plasma:
    heading = Markdown("### Plasma detected\n\n"
f"plasma lifetime of {plasma_lifetime:.1f} ms, from {t_plasma_start:.1f} ms to {t_plasma_end:.1f} ms")
else:
    heading = Markdown("### No plasma detected (vacuum discharge)")
heading

Plasma detected

plasma lifetime of 15.7 ms, from 4.4 ms to 20.1 ms

def show_plasma_limits(in_seconds=True):
    t_scale = 1e-3 if in_seconds else 1
    if b_plasma:
        for t in (t_plasma_start, t_plasma_end):
            plt.axvline(t * t_scale, color='k', linestyle='--')

$U_l$ management

Check the data availability

loop_voltage = read_signal(shot_no, 'U_Loop')
polarity_CD = read_parameter(shot_no, 'CD_orientation')
if polarity_CD != 'CW':                   # TODO hardcoded for now!
    loop_voltage *= -1  # make positive
loop_voltage = correct_inf(loop_voltage)
loop_voltage.loc[:t_CD] = 0
ax = loop_voltage.plot(grid=True)
show_plasma_limits()
ax.set(xlabel="Time [s]", ylabel="$U_l$ [V]", title="Loop voltage $U_l$ #{}".format(shot_no));

[Text(0.5, 0, 'Time [s]'),
 Text(0, 0.5, '$U_l$ [V]'),
 Text(0.5, 1.0, 'Loop voltage $U_l$ #44635')]

$B_t$ calculation

Check the data availability

It is as magnetic measurement, so the raw data only give $\frac{dB_t}{dt}$

dBt = read_signal(shot_no,'U_BtCoil')
polarity_Bt = read_parameter(shot_no, 'Bt_orientation')
if polarity_Bt != 'CW':                   # TODO hardcoded for now!
    dBt *= -1  # make positive
dBt = correct_inf(dBt)
dBt -= dBt.loc[offset_sl].mean()
ax = dBt.plot(grid=True)
show_plasma_limits()
ax.set(xlabel="Time [s]", ylabel="$dU_{B_t}/dt$ [V]", title="BtCoil_raw signal #{}".format(shot_no));

[Text(0.5, 0, 'Time [s]'),
 Text(0, 0.5, '$dU_{B_t}/dt$ [V]'),
 Text(0.5, 1.0, 'BtCoil_raw signal #44635')]

Integration (it is a magnetic diagnostic) & calibration

K_BtCoil = float(read_parameter(shot_no, 'SystemParameters/K_BtCoil')) # Get BtCoil calibration factor
print('BtCoil calibration factor K_BtCoil={} T/(Vs)'.format(K_BtCoil))

BtCoil calibration factor K_BtCoil=70.42 T/(Vs)

Bt = pd.Series(integrate.cumtrapz(dBt, x=dBt.index, initial=0) * K_BtCoil, 
               index=dBt.index, name='Bt')
ax = Bt.plot(grid=True)
show_plasma_limits()
ax.set(xlabel="Time [s]", ylabel="$B_t$ [T]", title="Toroidal magnetic field $B_t$ #{}".format(shot_no));

[Text(0.5, 0, 'Time [s]'),
 Text(0, 0.5, '$B_t$ [T]'),
 Text(0.5, 1.0, 'Toroidal magnetic field $B_t$ #44635')]

Chamber (+ Plasma) current $I_{p+ch}$ calculation

The Rogowski coil around the chamber measures the total current contained within its boundaries. Therefore, if there is plasma, it measures the sum of the plasma and chamber currents. In a vacuum discharge it measures only the chamber current.

Check the data availability

Because it is a magnetic measurement, the raw data only gives $\frac{dI_{p+ch}}{dt}$

dIpch = read_signal(shot_no, 'U_RogCoil')
if polarity_CD == 'CW':                   # TODO hardcoded for now!
    dIpch *= -1  # make positive
dIpch = correct_inf(dIpch)
dIpch -= dIpch.loc[offset_sl].mean() # subtract offset
dIpch.loc[:t_CD] = 0
ax = dIpch.plot(grid=True)
show_plasma_limits()
ax.set(xlabel="Time [s]", ylabel="$dU_{I_{p+ch}}/dt$ [V]", title="RogowskiCoil_raw signal #{}".format(shot_no));

[Text(0.5, 0, 'Time [s]'),
 Text(0, 0.5, '$dU_{I_{p+ch}}/dt$ [V]'),
 Text(0.5, 1.0, 'RogowskiCoil_raw signal #44635')]

Integration (it is a magnetic diagnostic) & calibration

K_RogowskiCoil = float(read_parameter(shot_no, 'SystemParameters/K_RogowskiCoil')) # Get RogowskiCoil calibration factor
print('RogowskiCoil calibration factor K_RogowskiCoil={} A/(Vs)'.format(K_RogowskiCoil))

RogowskiCoil calibration factor K_RogowskiCoil=5300000.0 A/(Vs)

Ipch = pd.Series(integrate.cumtrapz(dIpch, x=dIpch.index, initial=0) * K_RogowskiCoil,
                index=dIpch.index, name='Ipch')
ax = Ipch.plot(grid=True)
show_plasma_limits()
ax.set(xlabel="Time [s]", ylabel="$I_{p+ch}$ [A]", title="Total (plasma+chamber) current $I_{{p+ch}}$ #{}".format(shot_no));

[Text(0.5, 0, 'Time [s]'),
 Text(0, 0.5, '$I_{p+ch}$ [A]'),
 Text(0.5, 1.0, 'Total (plasma+chamber) current $I_{p+ch}$ #44635')]

Chamber current $I_{ch}$ calculation

R_chamber = float(read_parameter(shot_no, 'SystemParameters/R_chamber')) # Get Chamber resistivity
print('Chamber resistivity R_chamber={} Ohm'.format(R_chamber))

Chamber resistivity R_chamber=0.0097 Ohm

L_chamber = float(read_parameter(shot_no, 'SystemParameters/L_chamber')) # Get Chamber inductance
print('Chamber inductance L_chamber={} H'.format(L_chamber))

Chamber inductance L_chamber=1e-06 H

The chamber current $I_{ch}$ satisfies the equation (neglecting the mutual inductance with the plasma) $$U_l = R_{ch} I_{ch} + L_{ch} \frac{d I_{ch}}{dt}$$ Therefore, the following initial value problem must be solved to take into account the chamber inductance properly $$\frac{d I_{ch}}{dt} = \frac{1}{L_{ch}}\left( U_l - R_{ch} I_{ch}\right), \quad I_{ch}(t=0)=0$$

U_l_func = interpolate.interp1d(loop_voltage.index, loop_voltage)  # 1D interpolator
def dIch_dt(t, Ich):
    return (U_l_func(t) - R_chamber * Ich) / L_chamber
t_span = loop_voltage.index[[0, -1]]
solution = integrate.solve_ivp(dIch_dt, t_span, [0], t_eval=loop_voltage.index, )
Ich = pd.Series(solution.y[0], index=loop_voltage.index, name='Ich')

for I in [Ich.rename('$I_{ch}$'), Ipch.rename('$I_{ch}(+I_p)$')]:
    ax = I.plot()
ax.legend()
show_plasma_limits()
ax.set(xlabel='Time [s]', ylabel='$I$ [A]', title='estimated chamber current and measured total')
plt.grid()

Plasma current $I_{p}$ calculation

If there is plasma, the plasma current can be estimated as the difference between the total measured current and the estimated chamber current $I_p=I_{p+ch}-I_{ch}$

if b_plasma:
    Ip_naive = Ipch - loop_voltage/R_chamber  # creates a new Series
    Ip = Ipch - Ich
    Ip.name = 'Ip'
    Ip_naive.plot(grid=True, label='naive $I_{ch}=U_l/R_{ch}$')
    ax = Ip.plot(grid=True, label=r'using $U_l = R_{ch} I_{ch} - L_{ch} \frac{d I_{ch}}{dt}$')
    ax.legend()
    show_plasma_limits()
    ax.set(xlabel="Time [s]", ylabel="$I_{p}$ [A]", title="Plasma current $I_{{p}}$ #{}".format(shot_no));
else:
    Ip = Ipch * 0  # no current
heading

Plasma detected

plasma lifetime of 15.7 ms, from 4.4 ms to 20.1 ms

fig = plt.figure(dpi=200)
for I in [Ich.rename('$I_{ch}$'), Ipch.rename('$I_{ch}+I_p$'), Ip.rename('$I_p$')]:
    ax = I.plot()
ax.legend()
show_plasma_limits()
ax.set(xlabel='Time [s]', ylabel='$I$ [A]', title='estimated plasma and chamber current and measured total')
plt.grid()
plt.savefig('icon-fig.png')

Overview graphs and parameters

For convenience time is saved and displayed in ms, currents in kA.

df_processed = pd.concat(
    [loop_voltage.rename('U_loop'), Bt, Ip*1e-3, Ich*1e-3], axis='columns')
df_processed.index = df_processed.index * 1e3  # to ms
df_processed.head()

	U_loop	Bt	Ip	Ich
Time
-0.719783	0.0	0.000000e+00	0.0	0.0
-0.718783	0.0	-2.568271e-08	0.0	0.0
-0.717783	0.0	-2.704852e-08	0.0	0.0
-0.716783	0.0	-2.054709e-08	0.0	0.0
-0.715783	0.0	-9.039245e-09	0.0	0.0

if b_plasma:
    plasma_lines = hv.VLine(t_plasma_start) * hv.VLine(t_plasma_end)
    Ip_line = df_processed['Ip'].hvplot.line(ylabel='Iᴄʜ, Iₚ [kA]', label='Iₚ', by=[], xlabel='time [ms]')
else:
    plasma_lines = Ip_line = hv.Curve([])
layout = df_processed['U_loop'].hvplot.line(ylabel='Uₗ [V]', xlabel='', by=[]) * plasma_lines +\
df_processed['Bt'].hvplot.line(ylabel='Bₜ [T]', xlabel='', by=[]) * plasma_lines +\
df_processed['Ich'].hvplot.line(label='Iᴄʜ', by=[]) * Ip_line *\
   plasma_lines

plot = layout.cols(1).opts(
    hv.opts.Curve(width=600, height=200, title='', ylim=(0, None), show_grid=True),
    hv.opts.VLine(color='black', alpha=0.7, line_dash='dashed')
                        )
hvplot.save(plot, 'homepage_figure.html')
plot

Save each processed signal Series in a separate CSV file with Time and value columns

signal_files = []
for sig_name, signal in df_processed.items():
    fname = f'{destination}/{sig_name}.csv'
    signal.to_csv(fname, header=False)
    signal_files.append(fname)

units = ['V', 'T', 'kA', 'kA']

Markdown("Time series in graph in CSV format:\n"
         + "\n".join(f' - [{fn.split("/")[-1]}]({fn}) [ms, {u}]' 
                     for (u, fn) in zip(units, signal_files)))

Time series in graph in CSV format:

• U_loop.csv [ms, V]
• Bt.csv [ms, T]
• Ip.csv [ms, kA]
• Ich.csv [ms, kA]

if b_plasma:
    plasma_sl = slice(t_plasma_start, t_plasma_end)
else:
    plasma_sl = slice(t_Bt, None)   # TODO really use whole discharge ?
df_during_plasma = df_processed.loc[plasma_sl]
df_overview = df_during_plasma.quantile([0.01, 0.5, 0.99])  # use quantiles to skip peaks
df_overview.index = ['min', 'mean', 'max']  # actually quantiles, but easier to understand
if b_plasma:
    df_overview.loc['start'] = df_during_plasma.iloc[0]
    df_overview.loc['end'] = df_during_plasma.iloc[-1]
else:
    df_overview.loc['start'] = df_overview.loc['end'] = np.nan
df_overview.loc['units'] = units
# make units row first
df_overview = df_overview.iloc[np.roll(np.arange(df_overview.shape[0]), 1)]

df_overview

	U_loop	Bt	Ip	Ich
units	V	T	kA	kA
min	2.99702	0.143582	0.016303	0.325542
mean	6.96875	0.329785	1.16815	0.721699
max	12.8472	0.437052	1.90556	1.28779
start	10.2438	0.139055	0.00495779	1.07746
end	6.13906	0.438355	-0.0533577	0.645132

for agg in ('mean', 'max'):
    for quantity, value in df_overview.loc[agg].iteritems():
        print_and_save(quantity+'_'+agg, value)

U_loop_mean = 6.96875
Bt_mean = 0.32978
Ip_mean = 1.16815
Ich_mean = 0.72170
U_loop_max = 12.84723
Bt_max = 0.43705
Ip_max = 1.90556
Ich_max = 1.28779

#print_and_save('U_loop_breakdown', df_overview.loc['start', 'U_loop'])

#print_and_save('t_Ip_max', df_during_plasma.Ip.idxmax())